I must go to the chemist's for some medicine.

是正确的，for表目的，如：
Has a doctor ever given you a note to take to the chemist for some medicine?
医生给了你个条子，让你拿着去药剂师那里拿药了吗？
也可表达为：
I must go to the chemist's to get/buy some medicine.

对滴　for 表示得到.. 整个句子译为　我必须去牙医那里开些药

我必须去药店买些药。

扩展阅读：i got genshin ... where are you going ... the museum ... cloud music to mp3 ... what ... you must go now ... great ... right ... know ...