Leaving the Scene of the Accident, Will I Win My case?

I was returning home one afternoon when a former friend of mine made a left turn without yielding and T-boned my car. We both got out of the car and all of a sudden she ran back into her car and sped away. I was shocked that she would do this without telling me where she was going, I could not call her because I had no cell phone and I could not call the police. I waited for about a minute at the scene and tried to flag down cars however no cars stopped and it was dangerous to try and get one to stop. I decided to go home and Inform my parents, they told me to go to the police station and when I got there the Police said that the other driver called them to report that I had hit her and all of a sudden I sped away. The Officer said that when he arrived she was at the scene and I was not,therefore I left the scene of an accident, even though she left first. My car now has thousands of dollars of damage and is in essence totaled on top of that I am being ticked for leaving the scene of the Accident. The law In New York Says: if the other party is not present at the place where the damage occurred then he or she shall report the same as soon as physically able to the nearest police station, or judicial officer. That is what I did, but its nearly impossible to prove that she left the scene first. How can I beat this ticket ?