You should try convincing your mother to let you wear a binder... I mean, honestly, it's your body. I don't know how old you are, but regardless, I feel you should be able to make decisions about what you wear, not her. I mean, if you're going to look into a mastectomy and wearing a packer, why not wear a binder?
Argue that not having a flat chest could make you vulnerable to hate crimes, etc. It seems unfair.