Things I would check in your county/state and factors for you to personally consider:
Small claims court process and damage limits
Statute of limitations for filing property damage claim
Any state rules regarding insurance and/or body shop disclosure of accidents
Age/mileage of car
If accident had not occurred, what was plan for keeping/selling car (i.e. you always trade in at 100k miles, you always keep forever, you lease every 3 years, etc)
Time available to you for researching court process and/or finding legal counsel and/or proceeding with negotiations and trial
You HAVE suffered a damage, as any accident noted on a CarFax/equivalent lowers your cars value. If you have to pay annual property taxes on the value of the vehicle, this could be a consideration. If you were planning to sell in the near-term, this could be a consideration.
As others have noted, if the damage was visible but minor and non-structural (and the repair bill falls in line with this), the damage you've suffered was likely low in value. Combined with age of the car, you may be talking in the hundreds.
Without details, I'd guess its worth asking the insurance company for a couple hundred, they'll probably say no, and that will be that.
Full disclosure: I went through the DV process as described in (
Collision, Repair and DV/LoU Lawsuit: My Nearly 500 Days of Fun).