My mom pulls the "I'm the one who gave birth to you" card whenever I try to talk to her?

There is something wrong with your mom. She needs some help with counseling and maybe even a small amount of rehab. If you don't feel comfortable living with your parents, and you feel like your being abused, your able to go to your local court, and get some sort of paper signed by a judge allowing you to move out with another family member or friend that has a suitable and safe living environment as a 16 year old.