Hi, I am a nurse and huge traveler. You don't need any specific shots for Jamaica. However, the Centers for Disease Control (CDC) has a great travelers info page, you should check it out.
Vikki mentioned Hep B vaccinations, it's three separate shots over a few weeks, and if you haven't gotten it, you should just for your general health. Plus, a flu vaccine is always good to get in the fall. Your date is just after the peak of the flu season but if you have guests flying in they could bring it with them. Otherwise, bring hand sanitizer and use it on the plane, before and after you use the bathroom and when you touch public surfaces.