I am so doubtful about the sentence.
Because I think that could mean both.

One is, most people know well, that someone cut my hair.
The other is, I think it is possible in that the verb 'get' does mean just to transform a situation to another, that I cut my hair so that the hair was from a long to a short.

So we ought to write like this 'I cut my hair' to avoid misunderstanding it to the other case.