Alexandria is sometimes called the New York of the ancient world. That means you might very well use almost any ancient old-world language you like, as the people were incredibly diverse.
But the History of Alexandria shows a few 'preferred choices':
The early Ptolemies were careful to maintain the distinction of its population's three largest ethnicities: Greek, Jewish, and Egyptian. (At first, Egyptians were probably the plurality of residents, while the Jewish community remained small. Slavery, a normal institution in Greece, was likely present but details about its extent and about the identity of slaves are unknown.) Alexandrian Greeks placed an emphasis on Hellenistic culture, in part to exclude and subjugate non-Greeks.
The law in Alexandria was based on Greek—especially Attic—law. There were two institutions in Alexandria devoted to the preservation and study of Greek culture, which helped to exclude non-Greeks. In literature, non-Greek texts entered the library only once they had been translated into Greek. Notably, there were few references to Egypt or native Egyptians in Alexandrian poetry; one of the few references to native Egyptians presents them as "muggers." There were ostentatious religious processions in the streets that displayed the wealth and power of the Ptolemies, but also celebrated and affirmed Greekness. These processions were used to shout Greek superiority over any non-Greeks that were watching, thereby widening the divide between cultures.
From this division arose much of the later turbulence, which began to manifest itself under the rule of Ptolemy Philopater (221–204 BC). The reign of Ptolemy VIII Physcon from 144–116 BC was marked by purges and civil warfare (including the expulsion of intellectuals such as Apollodorus of Athens), as well as intrigues associated with the king's wives and sons.
Alexandria was also home to the largest Jewish community in the ancient world. The Septuagint, a Greek translation of the Hebrew Bible (the Torah and other writings), was produced there. Jews occupied two of the city's five quarters and worshipped at synagogues.
That means the most likely languages are by far not only Egyptian but also the wonderful Greek language, especially for the upper strata of society. This would also include the Jews, who were largely hellenised. But then from liturgical sources they would surely have also some curse and swear words derived from biblical Hebrew.
As for the Greek curses, swears, and insults,
you find that Aristophanes offers us plenty of Greek insults. Lots of them deal with feces, especially eating or shitting on others. Plenty deal with sex. Because Greeks compounded we have a lot of these that very directly translate into English, such as "koprophagos", "shit-eater" and "metrokoites", "mother-fucker", "kunops", "bitch (literally female dog)-face" or just "kun" or "kuna", "bitch" applied equally to men and women. The most common curse to a god is "ma Dia", "by Zeus", but you can find most gods' names in the accusative after "ma" for this like "ma Heran" or "ma Apollona".
And an even more colourful list:
ΑΝΑΣΕΙΣΙΦΑΛΛΟΣ: a promiscuous woman; one that dangles a penis [ανασεισίφαλλος = ανασείω + φαλλός]
ΒΔΕΩ: fart [βδέω = βρωμάω]
ΓΛΩΤΤΟΔΕΨΕΩ: using the tongue
ΓΥΝΑΙΚΟΠΙΠΗΣ: peeping Tom [γυναικοπίπης = γυναίκα + οπιπτεύω]
ΔΡΟΜΑΣ: prostitute that walks the street [δρομάς = δρόμος]
ΕΣΧΑΡΑ: a woman's genitalia [εσχάρα = από το ρήμα ίσχω (εμποδίζω)]
ΕΥΠΥΓΟΣ: a woman with a nice behind [εύπυγος = ευ + πυγή ]
ΚΑΣΣΩΡΙΣ: whore [κασσωρίς = από το κάσις (αδελφός, εταίρος)]
ΜΥΖΟΥΡΙΣ: a woman that sucks a penis [μύζουρις = μυζάω + ουρά (πέος)]
ΠΗΘΙΚΑΛΩΠΗΞ: a cunning man (slimy cunning) [πιθηκαλώπηξ = πίθηκος = αλώπηξ]
ΡΩΠΟΠΕΡΠΕΡΗΘΡΑΣ: a man who keeps on spewing nonsense
ΗΔΟΝΟΘΗΚΗη: a woman's genitalia
ΚΥΝΤΕΡΟΣ: someone without shame, a good for nothing person[> κύων]
ΛΕΧΡΙΟΣ: slimy [> λέχριος (λεχρίτης)]
ΛΥΔΙΑ: whore (Roman times, apparently because many high end prostitutes where from that region).
ΛΟΧΜΗ: bushy woman's genitalia [> λόχμη (θάμνος)]
ΣΠΟΔΗΡΙΛΑΥΡΑ: **** eater [σποδή (καταβροχθίζω) + λαύρα (απόπατος)]
ΧΑΛΚΙΔΙΤΙΣ: a very cheap whore, one that will do it for a copper
This would lead to many examples on the net.
The main research term to use is Aischrology:
Aiskhrología and the related verb aiskhrologéo refer to ‘shameful’ and/or ‘offensive’ language. Aischrology is a speech act which belongs to the vulgar register and causes offense by intentionally breaching norms of acceptable speech behavior. Although it is often equated with obscene language, aischrology also includes profane language.
Mark Janse: “Aischrology.” in: Georgios Giannakis (Ed): "Encyclopedia of Ancient Greek Language and Linguistics", Brill: Leiden, 2014. p76–86. (online)
The ancient researcher Pollux on the subject, mainly differentiates:
In a later entry from the Onomasticon, however, Pollux links the aischrologia wordgroup with the exercise of kakologia, loidoria, blasphêmia, etc.: here, by contrast, the dominant connotations seem to be those of socially dangerous abuse, insult, wrangling, and so forth, including the antagonisms of political invective. (Onom.8.80)
(Halliwell, p 118.)
A wonderful book on the subject would be Melissa Mohr: "Holy Sh*t. A Brief History of Swearing", Oxford University Press: Oxford, New York, 2013. It only starts in Roman times, but then Cleopatra is right at the line when Alexandria also became Roman.
If you insist on the girl being Egyptian and using that ancient language to curse, you still have plenty to choose from:
The first two recorded instances of what may be regarded as swearing come from Ancient Egypt. One of these is found on a stela, an upright stone slab with a commemorative inscription, dating back to the era of Ramses III, pharaoh between 1198 and 1166 BC.
The stela may be found in the Ashmolean Museum in Oxford. The inscription was written for a small tribe – probably named the Shamin – living in or close to the Dakhla oasis in present-day Egypt (cf. Janssen 1968: 165–72).
The inscription informs us that a certain local official named Harentbia donates a daily offering of five loaves in favour of his dead father. The offering is said to be ‘everlasting’ and promises that the official in charge of its execution will enjoy the protection of the god Amon-Re. It also describes the punishment that will be meted out to those who fail to follow the instructions: the person who fails in this respect ‘shall fall to the sword of Amon-Re’ and in addition ‘a donkey shall copulate with him, he shall copulate with a donkey, his wife shall copulate with his children’.
What makes the inscription interesting to students of swearing is the way the threat of retribution is worded. Sexual threats of the same nature involving a donkey turn up in numerous other legal documents and inscriptions from the same era. Donkey-based threats of this kind had apparently become formulaic and were used as a standardized ingredient in legal texts of the era (cf. Tyldesley 2001: 163). Amazingly, it – or something like it – is apparently still used as a standard curse in today’s Kurdish, that is more than 3000 years later than its first known appearance (cf. Demirbag-Sten 2005: 219).
Magnus Ljung: "Swearing: A Cross-Cultural Linguistic Study", PalgraveMacmillan: Basingstoke, 2011, p 45.
One suggestion, based on age of the protagonists, estimated timeframe Cleopatra, in Greek, and similarity to your Ergi might be along the lines of prokyon or catamite?
Thomas Conley: "Toward a Rhetoric of Insult", University of Chicago Press: Chicago, London, 2010.
Michelle Lovric & Nikiforos Doxiadis Mardas: "How to Insult, Abuse and Insinuate in Classical Latin", Metro Books: New York, 1998.
Ineke Sluiter & Ralph M. Rosen (Eds): "KAKOS. Badness and Anti-Value in Classical Antiquity", Mnemosyne Supplements,
Monographs on Greek and Roman Language and Literature, Vol 307, Brill: Leiden, Boston, 2008.
Ineke Sluiter & Ralph M. Rosen (Eds): "Free Speech in Classical Antiquity", Mnemosyne Bibliotheca Classica Batava, Brill: Leiden, Boston, 2004. (esp. chapter 6: Stephen Halliwell: "Aischrology, Shame, and Comedy", p115–144.)