Masturbating is perfectly normal for people. There is absolutely nothing detrimental about it. Your mother is being unreasonable, irrational. You're probably never going to get her to calm down.

I would continue doing your thing in private. Get another one and hide it better.

Fwiw her handling of this issue can cause issues now and down the road. I would highly recommend you see a counselor about it. If your mom won't let you see one, then when you turn 18 do it then.
When you're 18 move out and live your own life.