I need a bra, and it's really embarrassing to ask so how can I make my mom buy me one?

I have a flat cloth, bra but it's tight and it hurts when I wear it. I also can't wear certain clothes with it like fancy tops. When I wear it you can see the imprint of the front of the cloth bra on my shirt. Sometimes if I have a see through shirt i wear multiple undershirts but you can see the...lumpiness and roundness of my boobs. I don't want a push up bra or anything, but a normal small one so I can be comfortable. Also, I'm really uncomfortable with talking about this with my mom. It's hard to explain, but I feel like she won't let me. She doesn't even let me shave and she disapproves of me wearing deodorant, even though I have an organic one. You can see my buds even when I wear a lot of shirts, it sucks.