I had a similar accident in January 2003. I was driving with my son to his NYS DMV licensing road test of all things. We're stopped at an intersection, even though we had the green light, and other cars were stopped too, because a fire truck with lights and sirens was entering from a side street. I'm looking at the truck when a 16yr old kid with daddy's car skipping school plows into the back of me. My 94 Taurus was crushed up to the rear window by this kid's 1/2 ton puck-up. I had only 3-4 months earlier dropped collision on the car because of its age. Well the cops tell me it is 100% the other driver's fault. So I contact the other driver's insurance the next day to see what they were going to do about my car. For up to a week they tell me they have no record of their driver being in an accident and they don't believe me. So I fax them the police report, they contact the kid and his parents, and then tell me they will replace the car. They offered me $3500 for a car with a NADA retail of $3550. Not bad. But I counter-offered with a lot of reasoning $6000, and they accepted it. I was really happy over that. But looking back I wonder if they were anxious to get this behind them before I claimed injuries of some sort.
Now neither my son or me were hurt. But I was concerned with the jarring my head took when it snapped back and hit the head-rest. Why? I had Lasik about a week earlier. Although I didn't notice any effects, I still went back to the surgeon immediately just to have it checked out. I was OK. Still, NYS no-fault covered that
Although I'm sure you'll be OK on the property damage, I would be concerned about your pain now and some how try to protect myself. I too would consider the lawyer part. Lets face it, insurance's goal is to pay out as least as possible on every claim. They could care less about you