Your mom could probably report you as a runaway but would she? Are the cops going to race to find you? You won't be able to sign contracts (leases, car loans) yet. Can't get renters or car insurance if you need it. You can get emancipated but by the time you do you will probably be 18. You can finish school though and work. You just have to decide if it's worth it.
You do not have the right to move out without the consent of your mother until you reach eighteen. This is for your own protection, because you cannot get a credit card legally or be in a position to support yourself. However, you have a right to apply for emancipation as a minor if you have reasonable grounds to do so.