Translation:Can you help me buy medicine?
I'm still waiting for them to accept "buy for me."
When 帮 means “for” and not “help”
A common use of 帮 in Chinese is to talk about actions that are done for other people. The structure is exactly the same as above, but it doesn't mean “help” in English. This use of 帮 isn't about people co-operating to do something together (“help”), it's about one person doing something on behalf of another (“for”).
In (my) English, you generally cannot say "drugs" for Chinese medicine. "A drug" is something recognized by Western science as affecting the body. "Drugs" as a bare plural strongly implies illegal, recreational drugs. "Medicine" is more general and can apply to traditional Chinese cures.
No. This has nothing to do with American or British English. The "to" is simply optional in this structure. An infinitive does not need the "to" in many cases in English. "You need not use it here. I will not use it. You should not use it." Infinitive simply means uninflected for person, tense and number.