I am working on a story in which I wanted to include a character who was pressed into the British Navy in 1790's England, and ended up on a ship headed to the Caribbean. This is a pretty integral part of the story, so I want to make sure that it was even something that would have happened. Thank you in advance for your time.
Royal Naval vessels in the Caribbean, numbering 124 by 1718
The Royal Navy was engaged in war throughout the last half of the 18th century with every major power with colonies or interests in the Caribbean, the French, Spanish and Americans. The British also had their own colonies there as well, the British West Indies, so finding British vessels in the Caribbean is also historically accurate.
In fact if your sailor needs to be 'out' of the navy in the Caribbean, there is even history to back that up : The Hermione Mutiny
Yep, this is fine. In addition to mainland-based press gangs, the Royal Navy pressed merchant sailors including American sailors until the end of the War of 1812. The Carribean, of course, lies between Europe and North America, so perhaps an American pressed man would be particularly likely to end up there.