1) "cutting off my hair" would imply you are cutting your hair very, very short. For myself, I say it when I shave my head like here in my profile photo. For a woman, you might hear it said when very long hair is shaved or cut very short, like when donating your hair or selling it to a wig maker. "Cutting my hair" can be used the same way or more generally as well for any haircut.
2) I only see that spray used in football (soccer to me ^_^). My British friends call it "magic spray" because of the way players immediately jump up and are healed like magic from their fake injuries. It is a numbing cold spray which would help with a very minor injury but not do anything for a serious injury. I do not know if it has a proper name.