I came to the PI to revoker from back surgery last summer, and had a prescription for Valium that ran out while I was there (nobody checked my luggage, and I don't remember whether it was in a checked bag or carry-on--in multiple trips, no-one has ever looked in my carry-on except when leaving).
I was going to Doctor's Hospital in Davao for physical therapy, and my PT doc referred me to another doc there who wrote a prescription based on my empty prescription bottle and my story, plus the fact that my PT doc had sent me.
The pharmacy took a long time to fill it, and I was concerned that there was something unusual going on--I was actually a little scared--but eventually they returned with the pills.
I would suspect that if you have a prescription form your US doc and maybe a letter of explanation, you can get your Rx filled in the PI if you go to a hospital and find the right doc, like one who treats your disorder. The doctor visits cost $6.
Hope this helps.