I had a car accident with another driver. The crash happened when the other driver carelessly crossed the traffic, and my car hit that car on my own travelling lane. The other driver exchanged information with me but refused provided his car insurance company. My car had more damage and has been towed. I believe that the other driver has full responsibility for my loss, but he said I must work out with my own insurance company as he did. However, my car insurance has been canceled two months before due to late payments. What should I do to make a claim against that driver?