Make an appointment with a doctor (preferably a neurologist, or other brain related thing. The Taipei Hospital by Tower Records in Dinghao is a good place). Tell him you have depression and ran out of your medicine. (Got the bottle with the prescription on it? Great-bring it. If not, say you’ve been under treatment for however long, etc.)
They will ask you what symptoms you have, so mention something medically associated with your mental ailment (i.e. if you have OCD, say you are always turning water faucets on and off). They will then give you a month of your medicine (or an equivalent) and it will just be charged to your insurance card. Come refill time, you don’t even have to wait–knock on the door, say you need a refill, give the nurse your paper, no need to wait for your turn.
No insurance card? Go to that pharmacy by the West side of the 228 Park. It’s a pretty big place and you usually don’t need, um, prescriptions.