Help is a causative verb and the following verb should be short infinitive.
As for the passive voice, you should say:
I was helped to do something.
I agree. The first and second cases are examples of causative construction and ‘help’ functions as causative verb followid by an agent(me), So the action verb 'do' should be a bare infinitive(without to).
A verb--such as keep, promise, want, seem, and many others--that can link with other verbs to form a chain or series, is called a catenative verb; as: I want to try to remember to use that website.