Can I use with with help?
What does your sister always help you with?
Is it correct? (my English teacher said it was wrong)
This is correct as correct can be. Some people will argue that you cannot end a sentence with a preposition, but that "rule" was never really a rule, but stylistic advice modeled off Latin. In reality, like German, the preposition is just fine at the end.
If you were to rearrange it, it would sound awfully stilted:
With what does your sister always help you?
Despite what poorly informed grammar teachers once taught kids, this sort of style should be avoided today.
See Oxford Dictionaries's explanation of the subject.