You can but i must tell you first... their medicine you can't find in Singapore, Malaysia or Thailand. Your Singapore doctor issued prescription cannot be use there cos 99% can't find the medicine you want. The pharmacist there most of the times don't understand English, so if your Mandarin is also lousy then you will face a tough time buying medicine over their counter.
I know my dry cough need what type of cough medicine ingredients and how many mg for the main ingredient, over in Taiwan their active ingredient contents are higher than Singapore so when i consume it, it really effective. Sometime my cough accompanied with phlegm (white/yellow/brownish) i know what ingredients of cough mixture or capsule i need to buy.
If you don't know, then try asking... sometime their recommendation also quite accurate.