Look, I read about your situation. And the laws change depending on what state you reside in. In California, you must get a temporary restraining order first. You do that by going to the police in your city and making an application and paying a fee. That TRO is good for 30 days. Within that time you must file for a permanent restraining order. If you get the permanent restraining order petition delivered to the intended person who you are trying to restrain before the deadline then it stands until the court date. A permanent restraining order is issued after a judge hears the petition and decides on the matter. If a permanent restraining order is issued, then it lasts for up to three years. The judge decides on the time limits...
So, google it for your state.
Also, there are different rules in different states about reporting child abuse. In California, you could be liable for making a false report if Child Protective Services determines that there is no abuse taking place. In some states they take anonymous reports.
So, you're going to have to weigh the risks and benefits of making a CPS or DSS report. If you make a report and abuse is found your gf will be removed from the home, most likely. That isn't always the consequence even in California. Sometimes the court mandates treatment for the entire family and a therapist is sent in to do an assessment, provide family therapy, and provide individual therapy. Also, a case manager will work with the family to get wrap-around services for the family. Here in Califoria, CPS tries to keep families together when they can. If the abuse is extreme enough though, the child is removed from the home and placed into foster care.
If the mother is using a restraining order to shut you up about abuse, then see a family lawyer about it because if you report abuse, it might stop her from being able to file a restraining order. Then again, if the mother is agressive enough, it could backfire, depending on how good your legal representation is.
Proceed with care. Follow your conscience. You'll have to live with whatever you decide to do. I'd suggest finding someone you can talk to about the trauma you've been through personally. Try a high school counselor if you don't know anyone else. If anything a high school counselor can refer you to other help if you need it. Make sure you get enough support for yourself. You are also in need of protection and healing...