Yes, bring your old iPhone and get a new sim card. Just don't lose your regular sim card! When you buy your new card, it will come in an envelope; put your old card in the envelope and bring a quart size Ziploc to keep it in. There's an advantage in having a Jamaica number that you can give out freely and then don't have to worry about spam calls when you're back home. The Digicel plans can be confusing, but you can take a cheap plan then add money in small amounts as needed. Buy a few dollars' worth of cards for additional minutes so you have them handy if needed, then use any remaining ones as tips when you leave.

Be sure what your vendor offers on your current plan. "International calls" may mean calls from the US to other countries, but not calls made in other countries. They may offer a short-term expansion of your plan that will cover you. Also, be clear on roaming and data charges.

Personally, as we go back to Jamaica every year, we keep a Jamaica number active: every 3 months, I put the Digicel sim card in the iPhone, add the minimum number of minutes to keep the number active, then switch the sim card back. I think it's worth the convenience to have our driver know our number when we arrive, etc.; YMMV.