Huge amount of drug stores located in downtown. There are almost all medicine that you may need while vacation, from traditional Thai ointments to painkillers, like Nurofen.
If you take some special medicine regularly better buy for the whole holiday period or at least bring the original pack. Nobody can guarantee that there’s going to be absolutely the same medicine in Thai drug store, but seller would be able to offer you analogue.
Pharmacists speak pretty good English, so there must be no misunderstanding, while buying what you need.