Wow! I hate to hear what happened. Good luck if you decide to try to take it to court. My experience there has been that the cop and the judge are buddies, and you're screwed regardless of what happened.
I went to court once to fight a reckless driving ticket I got on my motorcycle, where I was stopped at a red light and made a quick move across lanes to avoid being rear-ended (I moved out of the way, and the car ran the red light). Cop sitting in a parking ran out and issued me a ticket, while letting the car go. In court the cop lied to the judge 3 times. I had witnesses, and when they "corrected" what the cop said, he just told the judge "that's right, I made a mistake, it happened like they said". End of the day, I proved I acted to avoid an accident which would have left me injured, but the judge sided with the cop and found me guilty anyway. I found out later that the judge and that cop were actually drinking buddies and could be found hanging out drinking together on most Saturday nights.