Is there any advice you can offer me to dispute these charges and perhaps get my money back?

I was in a car accident at an intersection where I was t-boned by another driver. There were no witnesses to the accident. I believe that she ran a red light. I had been stopped at a red, and when the light changed, I proceeded with my turn. That is when I was hit. After the accident, while we were waiting for the police to arrive I watched the light pattern and the two lights were never green at the same time. The police report relayed the facts from our statements, but did not provide conclusive proof of fault. The officer told me that when someone asks if they are getting a ticket, to him that shows the guilty party. The woman had asked if she would be getting a ticket. The only ticket that was issued was to me because I do not have insurance. I am a licensed driver but do not own a car. The car I was driving was my brothers and he does not hold insurance on the car either. When I tried to file a claim with the woman's insurance company, it was denied. The insurance company claimed that I was at fault because she was established in the lane. Now not only do I owe my brother for his car, the insurance company is coming after me to pay for the woman's car.