Unless you are cutting through tissue, your T will mostly likely not send you to the hospital. Hospitalization is acute care for someone who is suicidal, attempted suicide, or is psychotic. They could mention IOP or IP but you can't force a patient into either.
I think it is great that you want to tell your T! That is a huge positive step and you deserve to be free of SH. It's not easy. For me, I just came right out and told my T. However I told her with no intention of stopping so maybe thats why? I'm not sure. I did the same with my ED.
Sometimes it's easier to write a letter and have them read it in session. That way, they will start the conversation and you can just go along with it. I would recommend this method.
Keep up the good work!