(((CSC))) I know you are doing the very best you can for you and your son. Does his T think that he is suicidal and a danger to himself or others or that he needs to be hospitalized to get stable? Sometimes if the T is the one that calls and says their patient needs to be admitted the hospital responds better than you taking him in yourself.
I am sorry that he does not qualify for any other programs. I am sure you have looked into day treatments and other possiblities. From what you have described it sounds to me like he could have some BPD-traits.
You and your son are in my thoughts.
He is so lucky to have a mom like you.