For real prescription only drugs (e.g. antibiotics) apart from very serious stuff like morphine, you can buy them from a pharmacy in Singapore as an "export sale" without requiring a doctor's prescription (but subject to the discretion of the individual pharmacist).

You have to show the pharmacist your foreign passport and your plane tix departing Singapore within (if I recall correctly) 48 hours.

It's meant of course to cover situations where you previously saw a doctor in your home country, am in Singapore for a short period (so no time to see a local doctor) and require further drugs which were prescribed to you by your doctor at home.