I would sue, if it will not aggravate you even more to have to go to court. My husband and I were rear-ended by a guy who was behind us at a red light. We were behind another car. When the ligjht turned green, we waited for the first car to move, which he did not do immediately, but the car behind us misjudged and started to move as soon as the light changed. He went right into us and we were not yet moving.
So we called 911, to report the accident (we were not hurt, nor was our car, though the other driver damaged his own front end), but he lied to the cops and told them we stopped short. We could not have stopped short, we were at a red light to begin with. He just started to drive too soon. Fortunately, despite his lies, the law is on the side of the person who is hit from the rear. The irony is he came running out all apologetically that he was too close to us, he thought we were moving, he misjudged the distance, it was all his fault. I love honest people. BTW, I reported the accident, because I did not trust the guy to not report us as a hit and run. He looked sleazy to me, and it turns out my instincts were on the mark.