I have never travelled with a toddler either but I would probably recommend bringing some medicine or something.
You mentioned he had an allergy so I would definitely bring some childrens benadryl as you never know if he might have a reaction to something there, either something blooming, or bug bites, etc.
Maybe even some children's tylenol or things along those lines if her were to get sick or have a fever.

Just a thought.
I tend to overpack too because I always want to be prepared for everything.

But don't stress it too much. If needed, you can surely find just about anything (or at least a close facsimile) while in Negril.