What do you mean by "even if it is a phone from Jamaica"? Did you obtain it there? The phone you're talking about is a Sprint phone, correct? If so, then yes, you will get charged international rates for calls (see rates below) and texts ($0.20 cents per sent/received text) to Jamaica unless you have an international LD calling or texting plan. For more information, see http://shop2.sprint.com/en/services/worldwide/worldwide.shtml.
Check out a fun infographic that teaches you how to increase storage, enhance security, improve battery life and clean your device.