In Connecticut small claims cases are generally not appealable. Sounds like you had your day in Court. If there is some claim not addressed in the small claims judgment you may be able to pursue it in a civil lawsuit.
You can sue your insurance company for bad faith if it fails to fulfill its contractual obligation set out In your insurance policy. Some examples are failing to investigate your claim properly and offering too little money to settle your claim forcing you to sue. If you prove bad faith you may collect attorney fees and punitive damages in addition to the amount of your claim.