I am not sure I fully understand the fight that caused your recent split-up. But I imagine that you are harming yourself because perhaps you feel guilty for causing this mix-up. In your mind, you may think that harming yourself will accomplish several goals: 1) make yourself feel better (at least a little) because by hurting yourself you are punishing yourself for your mistake (probably because you think you deserve to be punished) or 2) because if your girlfriend would hear or see your bruises or pain and maybe, after seeing how upset you were, she would feel bad about ignoring your attempts to contact her and she would be more likely to come back to you.
If by this time she still has not returned your calls, perhaps you can try writing her a letter or sending her an e-mail. I am concerned with your self-abusive reaction to this split-up. I would suggest that you do the following: seek temporary help from a therapist who can help you appropriately plan how to re-approach your girlfriend and give you advice on how to save the relationship, or help you grieve this relationship if it is over (which I cannot imagine it would be over after just one fight). You also need to be in the company of friends and family to support you during this time so that you do not continue to engage in self-destruction. I hope that you can re-connect with your girlfriend but I also hope that you find a healthier way to deal with this situation. Please take care and be sure to care for yourself appropriately.