Towing company damaged my car, how do I make them pay for damages?

Your claim is against the towing company, not its insurance company. If you can't or won't hire a lawyer, the way to proceed is to write a demand letter to the towing company. They will probably notify their liability insurer about your claim. An adjuster should then contact you and ask you about the facts and for documentary evidence of your property damage. After that, the insurer will either negotiate with you or deny your claim. If you are unable to negotiate a settlement with the insurer, your only remedy is through suing the towing company. If the towing company ignores your demand letter, again, your remedy is to sue the towing company. If you had collision and/or comprehensive coverage of your own on your car, you should make a claim against your own insurer. This is first party, no-fault insurance, so you would not have to prove that anyone was at fault in order to get your insurer to honor your claim. Good luck.