Yes, talk to your state's Department of Insurance. They are there to protect you, it is their job to impartially review insurance complaints, and they do.
Keep a written record of all of your phone calls (answered and not) by date and time.
Keep a written record of any phone calls from the other part or their insurance (and when they identify themselves, decline to speak to them).
Keep all correspondence received from either insurance company.

I suspect the other party obtained one of the sleazy ambulance-chasing type lawyers who will file these claims because the personal injury money is so easy to get.

One little known fact about car insurance and accidents with little or no damage, is that most policies state they must be reported, because they need to know the current condition of your vehicle if it is involved in a subsequent accident.

Years ago I ran into someone at a stop sign. I was behind them and they kept starting and stopping, then started and were beyond the stop sign when they stopped again. I thought they were gone, and I hit them when I accelerated while checking traffic that was coming from a 45 degree angle to the road we were one, so I was looking back and not forward.) We did call the police and it was the policeman who noticed there was other damage to the other party's vehicle (no damage to mine) and when he pointed it out, then the other party "suddenly remembered" that they meant to say something about that. uh, yeah. Turns out a rental car hit them and they were having a hard time getting paid for it because the rental agency and the renter's insurance were trying to get the other to assume liability.
Anyway, so that is an example of why any damage, even if minor, needs to be on record.

I wish you luck and I hope you find a nice insurance company to change to.
I had my rates raised astronomically by a car-maker's insurance company, and declined to renew. I found very good insurance and great insurance reps through AAA (Triple-A).

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