Translation:Can you help me buy medicine?
Grammatically, the "to" should be there in English as it's part of the infinitive, even if Americans tend to drop it a lot.
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.
I've learned that often enough, Chinese people will say this when they want you to do this for them. They are just being polite about asking something of you
"Can you help me buy medication?" wrong? Is medication different than medicine in Chinese?