You can, up to a maximum claim of $7,500. Punitive damages are based on the net wealth of the defendant, so normally litigants don't request any amount, since the amount depends on the defendant's financial disclosures.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Call the insurance co. Speak to them about the overcharge. I have have some questions about your being able to sue for punitive damages as you are not the one who paid for the work /part and did not get what you paid for.
If you sue in small claims court, your maximum recovery if $7,500. It seems doubtful that you can ask for punitive damages because you did not pay for the repairs (the insurance company did) and as such, you do not have standing. Also, it is very hard to seek punitive damages because the conduct of the defendant (the body shop) would have to be so outrageous that it would have to be beyond all common decencies. Even if you could pass that hurdle, your recovery is still capped at $7,500. I agree with counsel that a better option would be to contact the insurance company that paid for the repairs.
Disclaimer: The statements made above do not constitute legal advice and these comments are not intended to and do not create an attorney client relationship.