When traveling abroad it's usually wise to take a basic first aid kit with you.
You don't need anything fancy - just a tin with a few bits and pieces that can help you out if you have an accident and need a temporary bandage or pain killer... until you can locate where the nearest source of medical attention is. If you are traveling to Jamaica, or anywhere else on vacation, there are some other things that might be useful to carry with you.
Some form of aspirin/Tylenol to help reduce fever or relieve headaches or muscle strains from sports your body is unaccustomed to. If you know that you intend to take part in water sports or new activities you may want to consider a pain relieving cream (or spray if you can find one that isnt aerosol based airline regulations apply here!).
An anti-bacterial cream to deal with any grazes or cuts that you may get taking part in activities, or even just walking on the beach if you stand on a sharp shell.
Hay fever medication even if you aren't known to suffer from hay fever, putting a packet of anti-histamines in your first aid box is just insurance against you finding out that you are allergic to a certain type of pollen and it's found in Jamaica!
Insect repellent! Anything that contains DEET should work fine. Pack this close to the top of the first aid kit and also carry one in your on-flight luggage in case it's a while before you get your bags once you arrive in Jamaica!
Sun block again this should be a spare for the one you have in your on-fight luggage.
Anti-diarrhea medication. As with the hay fever medication, you probably won't need it but it's better to take it and not use it, than not to take it and need it!
Bandage, and plasters for cuts and sprains. Take the "one size fits all" variety so that it doesn't matter where you hurt, your bandage or plaster will fit!
Thermometer even one of those little forehead strips that you can get for kids to check for fevers will be good enough to tell you if you've got a temperature or you're just a little unaccustomed to the tropical heat!
You should also pack any prescription medication you take, along with any syringes you need for taking it. Mark the prescription medication carefully, and include the prescribing doctor's name in case you are questioned over it at customs and immigration. Always carry two sets of prescribed medication, one in your carry-on luggage and one in the checked luggage so that you are sure that even if one set goes missing, you have a back-up.
Taking a first aid box on your Jamaica vacation isn't planning for the worst, it's providing insurance. You pay for it and you don't intend to have to use it but it's just good to know that it's there just in case!