Most likely, you had the assistance of an attorney in filing for the extension. You should consult this attorney concerning your question - or at least another immigration attorney, providing more details about your background.
There are a couple of things we need to look at here. First, have you ever overstayed a visa here in the U.S., even by a little bit? If so, even for a very short time, you may not be subject to one of the very severe bars to reentry - but you WOULD be subject to a rule that says that once you have overstayed, all future visa stamp applications must be made in your home country. If this is the case, obviously you couldn't apply in Jamaica if it isn't your home country.
If this isn't a problem, you can schedule an appointment - but here's the problem: handling visa applications from "third country nationals" - people from countries other than the country in which they are located - is discretionary on the part of U.S. consular posts. This means that they can choose to handle your H-1B visa stamp application, but they don't have to.
If this consulate chooses not to handle your application, you have no option but to go to your home country to make an appointment, apply for and get the stamp there - often with considerable delay. I recently saw a case where someone did this against advice, was refused and had to go to his home country, and ultimately was terminated by his employer because they simply couldn't wait any longer for someone to do his job.