score:2
Your doctor is correct that it is not a good idea (in terms of hassle).
However if you are only flying through TPE and not clearing immigration there, you will not go through the customs there. Thus so there will be no customs officers to look into your carry-on bags.
In KUL you would go through customs. All luggage and carry-on is screened there through an x-ray scanner. This seems to be very cursory check and I have never seen anyone stopped there so I have no idea what they're looking for. However legally it seems like you cannot bring them to Malaysia:
Prescribed drugs can only be imported into or exported from the country by virtue of a licence issued by the Ministry of Health, Malaysia.
Finally, your prescription from a non-Malaysian doctor is likely to be useless in Malaysia. I have tried my US prescription in different European countries, and it was never honored; you either need a prescription from a local doctor, or no prescription at all.
So to be safe, finish and ditch your bottle before clearing Malaysian customs. Hopefully you'll get well and won't need anything extra, but if you do, at least some Malaysian doctors speak good English and the visit is not expensive (by US standards).