Problem with out of state insurance after accident

Hello everyone, I live on Long Island, NY, and I recently had an accident at an intersection, I am not the one to blame, I had a green light, but the other car ran a red light and hit the front right side of my car. The driver of the other car was from a different state, turns out that in the police report it appears as an out of state insurance too. My insurance (GEICO) were useless in helping us find their insurance company, they said they had no power over that information and that they were not able to help us get our car fixed even if it was not our fault, that we had to contact the other guy's insurance. What can I do in this situation? At this point we harassed our insurance company and they did not help us.