Very Few US airports have International Transit Lounge.
MIA has (or had) one for American Airlines (AA) flights years ago, Not sure if its still there. I would check with the airline your are flying to and from MIA to see how that handle International to International, Flight,
Most US carrier make you clean customs/immigrations in MIA, so you would go out of MIA as a domestic flight.
You should contact the US embassy in Jamaica to see what the requirement are for a Transit Visa.
General Information | Embassy of the United States Kingston, Jamaica