There is online e-pharmacy in Singapore. I know of 2:
www.mypharmacy.com.sg which is Changi Hospital and
www.ttshpharmezy.ngh.com.sg which is Tan Tock Seng Hospital
They have been around for years, you can get prescription meds and most pharmacy stuff, devices, machines, wheelchairs, walking stick etc on line and they will deliver for a fee or free delivery with a certain amount purchase. It has been very useful for caregivers to bedrest patients.
Check out the websites for more info. I doubt you can purchase any prescription meds without a prescription from a doctor.
I'm sure they don't sell fake meds, I think they were originally set up by the Govt hosptials for the convenience of busy working care givers who can't afford the time to Q at hospitals for prescription meds or transport home care items for their bed ridden loved ones.
I've purchase online at these websites before. It is easy and convenient. You might want to check out the actual pharmacies at Changi hospital and Tan Tock Seng hospital to confirm exactly what you want, then buy them online.
PS- I just checked on prescription meds on both websites, it appears to be only for refill.