I got very depressed when I was about his age and told my mom I wished I'd never been born. I reasoned that that would be better than dying because I was afraid of death. So sorry you and your son are going through this. It sounds like you're on the right track, though.
My advice is to not be afraid to keep looking if the first therapist isn't helpful, as they all have different personalities and techniques, and stick with getting help for as long as your son needs it. My mom only took me to one session and didn't like the counselor. She was in huge denial, I guess, as even my pediatricians kept trying to tell her I was depressed. But she didn't want to admit there might be something wrong with our family dynamics. I really wonder how my life might have been different if I'd gotten the help I needed for mental health issues at an earlier age instead of now, in my 20s.
Also I remember being afraid to be honest with the counselor because my mom was right there sitting beside me the entire time, and I didn't want to upset my mom. They had me go sit in the car for maybe 15 minutes at the end so they could talk in private... which made me feel really weird and kind of mistrustful.
I'm not saying to avoid these things or that your son will feel that way, and I'm not trying to make this post all about me

... just trying to give you a different perspective. I probably would have felt better if someone told me that they'd kicked me out because the counselor was telling my mom how to help me, not saying bad things about me or whatever. And it would have been nice if I'd been able to talk to someone alone or even asked me if I wanted my mom to stay.
Oh, and I also hated school with a passion and wanted to run away. Feel free to PM me if you'd like.