A medical doctor would be great. A mental doctor would too, because apparently therapy isn't helping. I wish you'd just talk to her and maybe she could help you. or maybe you just need to find someone new. But yes, by all means, go to a doctor (psychiatrist or "regular")!!
I just don't think you really want to die. I mean, I know you feel that way. Trust me I understand, because I've felt the same way, but deep down inside, there's part of you that doesn't want to die and doesn't want to continue to hurt herself like this. So please get someone to help you!!