If your parents consent, you probably can move out. You could look at emancipation, but it's a process that takes several months and you might be 18 by then.
Ask your mom If she'll do some family therapy with you before you move out.
This answer DOES NOT establish an attorney-client relationship. This answer is based on the limited information provided and is not intended to be conclusive advice. There are likely other factors that might influence or change the advice after a more lengthy consultation.
It is called Removal of Disabilities of Minority in the Texas Family Code. It would cost money and take time to do. Why don't you just ask your mom to meet you somewhere wnere the two of you can sit down and talk about these things.
This does not establish an attorney/client relationship