Therapy or mental health hospital?

I'm really stuck and I need help. I'm trying to decide if I should start with therapy or go straight to having my 16 year old admitted. His behavior started spiralling a year ago. He deals with an absent father who constantly flakes on him. He grew up watching his dad emotionally abuse me so I think that's why he doesn't have much respect for women. He started getting into more fights at school. Then I found out he was having sexual relationships with multiple girls and cheating on all of them. He would yell. Call me out my name. Punch holes in the wall sneak out to have sex. He started getting labeled a fuck boy because of how badly he was sexually acting out. He also did molly with a friend but from everything I know that was a one time thing. We had a very emotional breakdown today because one of his friends moms told me he cuts. I asked him about it and we started yelling at each other so I grabbed his arm for myself and pulled up the sleeve and he had been cutting. That's when he started crying and he doesn't cry. I held him while he cried. Is starting with therapy the move or is self harm serious enough where we should go to a mental health hospital