Can I sue the person I ran over if I was not at fault for the accident?

Question Details: I was involved in a traffic event which resulted in my running a lady over. She was injured and my car was damaged. The police report confirms that no driving offense was committed and I was not at fault. I have received quotes in the region of $10,000 to repair my car. What legal rights do I have to pursue the lady I hit? I've suffered/suffering substantial financial losses and the whole event has effected me. I have not driven since and the even has knocked my confidence drastically.

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