The other answers have mentioned a lot of other people and events that your school should have told you about. I'm going to tackle this from a slightly different angle, and try to explain why you're experiencing this problem - and you are definitely not imagining it.
You summarised the curriculum as segregation, slavery and 3 civil rights icons. Believe it or not, the curriculum you're being provided represents an advance on what it was like before. It did not used to be a sympathetic portrayal, of civil rights heroes, and black people's defeat of de jure segregation. Not even a superficial one.
Until the 1930s, the Dunning school of post-Civil War American history was academically dominant. A summary of this school:
All agreed that black suffrage had been a political blunder and that the Republican state governments in the South that rested upon black votes had been corrupt, extravagant, unrepresentative, and oppressive. The sympathies of the "Dunningite" historians lay with the white Southerners who resisted Congressional Reconstruction: whites who, organizing under the banner of the Conservative or Democratic Party, used legal opposition and extralegal violence to oust the Republicans from state power. Although "Dunningite" historians did not necessarily endorse those extralegal methods, they did tend to palliate them. From start to finish, they argued, Congressional Reconstruction—often dubbed "Radical Reconstruction"—lacked political wisdom and legitimacy.
It wasn't until the 1960s that the Dunning school was discredited, and not until the 1970s that new interpretations emerged. The two interpretations now current are essentially a) that reconstruction was a good but failed attempt to remedy injustice, and that civil rights legislation has fulfilled its potential, or b) reconstruction failed because it was inadequate, and civil rights legislation still has not realised racial equality because it hasn't gone far enough.2 From the 1970s to the present day, a) was more influential in school because it was less controversial and more palatable ('it was bad but everything's fine now'), and that's essentially what the system is trying to sell you.
School history curricula are inevitably simplified versions of academic history's consensus, but they also tend to lag behind it. This might help to explain why people like Donald Trump, who went to school in the 50s and 60s, say things like the Civil War was a failure to compromise, as if Abraham Lincoln was somehow partly to blame for opposing slavery (I'm not making excuses for Trump -- most people of that era would think a bit more critically instead of repeating the propaganda of their youth). Likewise, the idea that the civil rights era made everything fine now is looking a bit ridiculous, but your curriculum has not yet caught up.
As you've noted, although shallow, the current history curriculum celebrates Martin Luther King and other civil rights heroes. Obviously the civil rights era led to this change -- the Dunning school was a tool for entrenching segregation. Most people would agree that a curriculum which celebrates MLK is less noxious than one that celebrates Robert E Lee. However, this leads to my next point: the study of history shouldn't be employed to celebrate a national story, however benign.
This article is a comparative study of history education in the USA and Northern Ireland. It's about primary school (elementary school), but the observations are still relevant.
The differing nature of historical representations in the two countries, however, leads students to contrasting conclusions about the purpose of learning about the past: in the USA, students emphasise that history is important so that they will know about the origin of their country and their own place within it, while in Northern Ireland students describe the purpose of history as being to learn about those who are different from themselves.
These students consistently used pronouns such as ‘ our’ and ‘ we’ in talking about history; for them, history was important because it helped them understand how their country began and how they should treat each other. Reflecting the family contexts in which they had learned about the past, students thought they would one day hand this information down to their own children. But these were not the reasons students in Northern Ireland gave for studying history…
[T]he most frequent reason students gave for learning history was nearly the opposite of US students’ rationale: history is important in order to learn about people who are different. Year 8 student Hamish put it succinctly— he said that history is important ‘to understand the way other people lived and went about their daily life’ . This theme ran throughout students’ explanations of the rationale for studying both particular topics in history and the subject in general; they consistently pointed to differences between past and present— the more differences the better— as the reason for their interest in history.
In the USA, the history that students encounter in public forums (whether schools, museums or cartoons) is almost always a story of national development: students learn about the original inhabitants of the Americas, their conquest by European explorers, the colonisation of the Eastern seaboard, the fight for independence from Britain and the development of the new nation— increasing prosperity, industrialisation, geographic expansion and the extension of rights and opportunities to new sections of the population.
The historical figures children encounter from a young age are people who play a role (albeit sometimes mythical) in this story of progress and national development— Christopher Columbus, George Washington, Betsy Ross, Abraham Lincoln and Martin Luther King. Sometimes the nation’s past is presented in a positive light, and sometimes it is portrayed more critically— but whether positive or negative, history in the USA is invariably the history of us, the history of our nation. Learning about others— about medieval Europe or ancient China or the Malian empire or even the Aztecs— is rarely a part of young children’ s encounter with history; such peoples are not often represented in school.
At the same time, US educators must consider the limitations of history that focuses too exclusively on identity. Stories of who we are typically also become stories of who we aren’t: establishing loyalty to a community usually means denying others as lying outside that group. Such exclusiveness may be useful when trying to establish pride in the unique experiences of a particular community, but when the past of an entire nation is under consideration, narratives which focus only on limited sections of the population will exclude many whose experiences deserve to be recognised.
In the USA, the story of the nation’ s past has for too long ignored or minimised the role of women, minorities and working people, and as a result national history— and national identity— have been equated with the limited interests of a small segment of its citizens. In this study, students’ explanations that studying immigration and the Civil Rights movement teaches us how to treat them suggests the limited horizon of their sense of American identity.
Another article (same author and topic, but different article) shows the consequences of the US approach to history education:
Based on this research, students in Northern Ireland appear to have a more developed understanding ofthe role of historical evidence than do students in the US. Most of the US students in these studiesappeared to treat historical sources simply as information, a perspective also identified among some English children in the work of Shemilt (1987) and Lee, Ashby, and Dickinson (1996). US students thought that people in the past knew what was going on around them, and they passed that information along to us, either through oral transmission or through books. Even when students talked about the use of physical remains and artefacts, they treated such remnants of the past simply as sources of information. They thought that old uniforms or muskets would show what old uniforms or muskets were like, but there was no suggestion that these could be used inferentially as evidence for a historical account. Historical sources, then, were simply seen as a means of direct access to the past. Although many students in Northern Ireland also saw oral transmission (but not books) as a source of knowledge, they typically combined this with a recognition of the role of other sources. Moreover, the way they referred to these other artefacts and remains indicated at least an initial understanding that they could be used as evidence, not simply as sources of information.
I am not suggesting that history teachers or education officials in Northern Ireland are morally or intellectually superior. There is a reason they've focussed their curriculum on distant times and places, as these articles note, and it's not because they can do more intellectually sound history. It's because the history of Northern Ireland is literally explosive, and history educators understandably don't want to prod it. It's a happy (and surprising) coincidence that this unhappy situation leads to more robust history education. I'm from the UK and a former teacher - US educators certainly aren't alone facing pressure to shape history education to the requirements of exceptionalist propaganda. Things have got worse in England in that regard; it's a longstanding problem in [Japan].8
You've astutely spotted some of the holes in the history education you're being provided. My advice would be: try not to think of history as just a story of how things came to be as they are. Learn about the past for its own sake, and it will benefit you in ways you didn't expect. How are you supposed to know what you need to know, until you know it?