You can get inked here, but two things to consider tht may change your mind:
Swimming - whether it be a pool, fresh water or salt water - should be avoided for at least 2 weeks.
Scabbing and Peeling
After a few days, you will notice some peeling and possibly a little scabbing. Excessive scabbing could indicate a poorly-done tattoo, but a little is sometimes normal and there is no need to panic. Apply warm moist compresses to the scabs for about 5 minutes 2-3 times a day to soften them and they will eventually come off on their own. (Do not apply ointment or lotion to a softened scab - wait for it to dry) You will also start to itch, just like a sunburn when it begins to heal. The advice here is, don't pick, and don't scratch! If the skin itches, slap it. If it is peeling, put lotion on it. And if it is scabbing, just leave it alone. Your tattoo is almost healed, and now is not the time to ruin it!
Protection from the sun
After your tattoo is healed, from now on, you will always want to protect it from the sun's ultraviolet rays. These can fade and damage a brilliant tattoo very fast. Before spending a lot of time in excessive heat, protect your tattoo with a minimum 30SPF sunblock.
So you will have to avoid swimming and avoid the sun while in Negril after the tattoo...
