My mom refuses to help me get help for my bulimia because she thinks I'm lying. Please help!?

I have been for three years. I did it to have some control in my life. And I have severe issues with self image. I understand that I need help and so I finally got up the courage (it took me three months) to tell my mom. And then she said that I was doing it for attention. I was like, "Umm I kept it a secret for three years, if I wanted attention I would've made it a big deal!" And then she was like, "oh come on gimme a break you just made it up just now, I've never heard you throw up, I bet your too scared to stick my fingers down your throat." And I was like "first of all why would I make that up? Second, I obviously didn't do it whn you were around and you learn to not make noises when you do it alot. And third, you want me to ******* show you? Because I'm extremely capable." And she STILL thinks I'm making t up and she doesn't want to spend money on residential treatment (which is the only thing that will help at this point) or just simple therapy because she insists I'm lying and she doesn't wanna waste her time and money. I'm just trying to get help. I'm so scared that this disease is making me spiral out of control and I can't really treat it until my mother believes me, what do I do? Its gotten to the point where i purge three or four times a day. Thanks