I share your concern. Your daughter didn’t give therapy a fair chance. A depression that has been building for 4 years needs more than 4 visits of attention from a therapist. It may be that she didn’t connect well with the therapist. It may be that she is so discouraged that any therapist will have a tough time engaging her.
For that reason, I suggest you go to therapy with her — not because I think you have a mental illness (I don’t) but because sometimes people need the support of people who love them to jump start treatment. If she won’t go, please go anyway. There is little I can recommend on the basis of a letter. But a therapist will be able to hear your whole story and may be able to give you some concrete suggestions about how to help the daughter you love.
I wish you well.