Dear Christopher,
No, an Rx from your US physician will not qualify here, you will need to see a local Panamanian doctor and get a local rx from her (you can ask your home doctor to communicate with your Panama doctor). Narcotics and antibiotics are among the meds that do require a prescription here; with other meds if they are not considered addictive or harmful when not closely monitored (like Ventolin sprays for asthma, for example), the pharmacists here can be quite lenient about prescriptions.