Hi, I'd like to help you with your question.
There could be a few different things going on here with your girlfriend.
It sounds like she may either have a personality disorder or she has a history of abuse and reacts to closeness with another person by pushing them away.
Someone who is abused as a child or in early adulthood can react to closeness by being afraid. Their first reaction is to protect themselves so they push the other person away. Your girlfriend may have past abuse that causes her to feel this way and that is why she treats you as she does. Therapy can help but if she is unwilling, then there is not much you can do to help but be supportive and learn what you can about past abuse victims. That way, you do have choices in how to respond.
Without knowing more symptoms I can only provide an educated guess, but she could have borderline personality disorder and maybe traits of narcissism. I can provide you links that include symptoms and you may be able to match her symptoms up to the lists to see if she sounds like them.
In the case of a personality disorder, most people have little to no insight into their behavior. When you try to present their symptoms to them, they usually either have an excuse or they put the problem back on you and blame you. Getting help for someone with a personality disorder is difficult at best. They usually have to see that they have a problem before they will seek therapy. Or they come to therapy with another problem such as depression and the personality disorder is treated along with the depression.
Personality disorders are usually developed in response to abuse in the past. The person handles the abuse by developing personality traits that allow them to live with what happened to them. It is a way of seeing the world that makes it easier to live with.
The best you can do is keep trying to offer your girlfriend help. Suggest she talk to her doctor. He/she may be more influential in getting her to see she needs therapy. Maybe her parents or other family or friends can also help you convince her to at least get an evaluation.
Here are some links to help you with personality disorders:
Difficult Personalities: A Practical Guide to Managing the Hurtful Behavior of Others (and Maybe Your Own) by Helen McGrath PhD and Hazel Edwards MEd
The Cognitive Behavioral Therapy Workbook for Personality Disorders: A Step-By-Step Program (New Harbinger Self-Help Workbook) by Jeffrey C. Wood
You can find these books on Amazon.com or your local library may have them for you.
Remember to care for yourself while coping with your girlfriend's behavior. If it gets too much, consider taking a break yourself. If you choose to continue the relationship, talk to friends, family and a therapist if you feel it would help. When someone you care about is suffering, it can be very stressful. It is much easier to help her if you feel ok yourself.
I hope this has helped,