You have made positive steps. GP has offered great help.
Each child is so different.
When my child was depressed and self harmed at nearly 15, this is what I did. Visited GP who refered my child, but no councelling was offered, said it was a school bullying problem and resolve it at school, but that's another story.
So I decided to try some other ideas to sort things out. She spent a lot of time in her room (like most teens), and it was a kind of a no go area for me (she told me to stay out), so I cleared out her room one day when she was out at school and I had a day off work, top to bottom, removed all old clothes and things she no longer wore, loads of old junk and old bits of rubbish, bought her some new bed linen etc. Didn't peek in diaries, notes, letters. Just didn't touch them. Very hard but knew it was for the best.
For most teenagers their rooms are private. But I decided to clear it out, for her as it was a burden to sort out and continually getting messier by the day. My doing it helped her feel comfortable again in her surroundings and able to manage it, and so start to manage herself. She is improving bit by bit. Still gets very low. Maybe you could suggest you do it together and he has places that he does and you don't touch, it might help.
Hope this bumps thread for you and also I know how sad you must be feeling. There are a few threads you could search on MN or look back further in the teen threads and find some more helpful answers.