If as a result of the accident you were not ticketed and the other driver was that is the general determining factor of fault. You would be best served by reviewing the police report it often will spell out fault. If not you can contact the police department to verify.

Once you do that the party at fault will be liable for payment of damages. If you have a problem recovering than you have to decide whether to pursue the matterlegally and if so find a local attorney to assist you. Good luck with everything