The doctor doesn’t have a pharmacy attached? That’s bullshit. How can he prescribe a drug that no one has? Unless you tell us the drug we can’t help too much.
You could go to Google maps, search for likely local pharmacies, and start calling them. There’s probably some kind of Taipei City service though, I’ll take a look.
I use this place. They’re pretty big and always have what I need. I don’t know how to write the address, but just call them and ask if they have it. They’re in Taipei City.