I checked my bank information to answer this question for you. I went to Andrews Memorial Hospital in Kingston in December 2015 and paid the following amount by credit card. The amounts shown below are in US dollars. You will pay in Jamaican dollars if you pay in cash.
Exam fee $127
Additional vaccine cost $28
I looked at the following website and the costs in Jamaican dollars as of today are following:
Cost for Medical Examination
15 and over J$23,320
14 and under J$8,850
It does not seem that there is a way for a sponsoring person in the US to pay for the fees in advance online. If you show up to the medical exam with your fiance, then you can pay the costs by your credit card.