Try Freetown Drug Store in Belize City. Their prices and selection are much better than on the island. You can send money and he'll send things out to the island for you same day on Tropic Cargo. phone # 223-1373
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.