I would call your cell service provider (eg, Verizon). Tell them where you are going and find out what the best plan update you need for what you need to do and for the length of time you will need to do it.

Some people just get phones there or just sim cards for their phones. Too complicated for me... Some drivers and some resorts may even provide a phone for you to use - GeeJam does it, not sure if anywhere in Negril does.