If you are using the blackberry messenger there is not any additional charges...If you call a phone number in Jamaica it will charge you by the minute or per text message if you send sms text messages with out an international text plan
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.