Sexual Abuse Support Group
Sexual abuse is a relative cultural term used to describe sexual relations and behavior between two or more parties which are considered criminally and/or morally offensive. Different types of sexual abuse involve: Non-consensual, forced physical sexual behavior such as rape, incest or sexual assault, or psychological forms of abuse, such as verbal sexual behavior or...

Is therapy or counseling an option for you now? If so, please go for it. It will be a valuable support and once you have the right therapist/counselor (which is not always the first one you see) you will be able to start healing.
As for the situation with this girl, it doesn't sound good that she treats you like dirt. You deserve better than that. Please don't get into an abusive relationship that will reinforce the idea that abuse is what you deserve and that's all you can get. And if someone pushes you over the edge and you lash out, then you will be considered a delinquent or criminal and possibly be abused by the system. It's a bad direction to go in!
I think you can set some boundaries on how she treats you, and if she does something hurtful or disrespectful, tell her "That's not okay, don't treat me like that." If she likes you she may change her behavior. And if she can't or won't change her behavior, your best bet would be to move on. There will be someone better down the road.
Basically, the best way to approach any relationship is to build friendship and trust. If this girl is just getting off on her power to affect you and doesn't care if she hurts you, she is not the right person for you. There will be someone else, someone better for you, down the road. But if you refuse to accept being treated badly, she might just stop treating you badly.
You say that being touched not something you can stand right now. I think and hope that with the right person you could learn to feel differently about it - but that change would have to start with your feelings being respected right now.
You might find it helpful to look at these sites. Both have a hotline and a chatline that you could use.
1) RAINN.org The hotline here helped me find a therapist to work with recovering from sexual abuse.
2) 1in6.org This is specifically for men who have been sexually abused.
I also want to say that your existence being a result of rape is in no way your fault and doesn't mean anything about you. You were born as innocent and as worthwhile as every other human being on this planet. You deserve love and respect as much as everyone else - we all do.
Therapy or counseling is not an option right now. I have a counselor at school but it stays on the subject of school
I don't feel like I deserve better than the way she treats me. When she calls me names it feels familiar and right. Shes hurt me but I don't say or do anything. I know I should make it clear that she shouldn't but in my mind she wouldn't do those things if I didn't give her a reason to
I want to make this work with her
Is it common to not want to be touched or am I being extreme?
The last part I don't know what to say. It hits a sore spot
Is it common to not want to be touched? I think it is. The degree varies. I think most of us know that the wrong kind of touch can feel very molesty. But when you are with someone who is loved and trusted, it is normal for touching to be mutual. That is something you probably want to work towards.
Are some people to broken or worthless to be loved?
As to question one, I think you need a trusted partner to work with you, starting from what you feel comfortable with, and slowly moving that line little by little.
You have mentioned that she encourages you to open up. That sounds like an invitation to get to know you better. I invite you to share a little of your past and give her the benefit of the doubt. You might be pleasantly surprised.
I want to share a little bit of my experience. I used to feel suffocated when dating. I broke up with my boyfriends monthly and sometimes weekly. Now, I only have wonderful memories of these wonderful men.