Wow. That is rough stuff. I'm torn here about what to say. Seems like it might be best to keep it to yourself and spare him any more pain and worry right now, but then if he finds out later, that could be a serious blow to the trust in your relationship.
If you do tell him, make it clear that SI is not the same as being suicidal. (I'm making assumptions here, but you have not mentioned wanting to die here, just feeling like you need to hurt yourself.) Those are two different things that can get confused and scare people even more and if suicidal feelings are a part of it, please get help.