Bra problem for a newbie!! please help x

Okay so I'm 13, I started growing boobs at like year 5?? and up until middle of year seven i had to wear those useless crop top things!!! my mum allways tells ne that I'm too young for all this! and when she finally gave in she got me one of them material non cup non wire things? okay it's an improvement but I have quite large boobs books for my age and it doesn't even support me. all the girls in p.e keep making fun of me because of it, I have told my mum she says I'm being soft and need to toughen up and that I'm to young for a 'big girls bra' wtf!! I just really need the right support, any suggestions??? ((((((((((by the way))))))))) I'm not at all making my mum look like a bad person I love her sm but I wish she'd just listen to me about this x