What you should do is retain and speak with a criminal defense attorney IMMEDIATELY. Hitting your girlfriend and breaking her nose is a crime--assault; you are potentially compounding your offense by adding "fleeing prosecution" or a similar act to what you are liable for. Experienced criminal defense attorney can advise you as your best course of action, represent you to the police and prosecution, as well as in court, explain in the most reasonable way possible why you fled, and maximize your chance of minimizing any punishment. Do NOT speak to anyone about this matter before you speak with your attorney.