Depends on your definition of an arm and a leg and how quick you need it. AA has priority parcel shipments from MIA to Belize City for $125 for packages 1-11 kg. You drop off in MIA 2 hours before departure and pick up in Belize City 4 hours after arrival. The 4 hours is probably on the high side for customs to release it. You should be able to put medication in a small cooler with some ice and stay under the 11 kg. Stay away from using dry ice as it is considered a dangerous good and will cause the price to go way up.
Last edited by tahunt; 02/11/15 10:28 PM.