How is a college student supposed to move out with no co-signer and no credit?

So i thought ive been gaining credit on my car ive been paying 270 a month for...but when I try to get credit cards, they deny me 'due to credit' so I dont know if i have enough or if my mom managed to mess it up. I have an amazing job with our state as a student istant, im 20 and can afford rent and bills easily but my mom for instance just had her car reposessed tonight and is horrible with her money and has bad credit. How am I supposed to get away from her using MY name for her bills she cant pay if I cant get approved when I apply for apartments? =(