Traveling to Jamaica should not adversely affect your health. Finding a good doctor in Jamaica is no real problem, and all of them speak English, of course.
Keep the following suggestions in mind:
Although piped water is safe, it's probably best to drink bottled water in Jamaica.
If you experience diarrhea, moderate your eating habits and drink only bottled water until you recover. If symptoms persist, consult a doctor.
The Jamaican sun can be brutal. Wear sunglasses and a hat, and use sunscreen liberally. Limit your time on the beach the first day. If you do overexpose yourself, stay out of the sun until you recover. If your exposure is followed by fever or chills, a headache, or a feeling of nausea or dizziness, see a doctor.
Some of the biggest annoyances in Jamaica are the insects called "no-see-ums," (sand flies) which appear mainly in the early evening. You can't see these gnats, but you sure can "feel-um." Screens can't keep these critters out, so carry your favorite bug repellent.
You don't need to get any particular shots or vaccinations to travel in Jamaica, and most common medicines are available over the counter. If you need special medication, however, try to arrive in Jamaica with an adequate supply for the duration of your trip.
If you're traveling in the countryside, it's wise to take a small medical kit with you containing antacid, antiseptics, calamine lotion, Band-Aids, sunscreen, lip balm, water purification tablets, and insect repellent.