Car hit by uninsured driver - how to recover the costs?

Can you know any reasonably priced (if you will find any) health insurance companies?
"I accidently hit a vehicle that was parked. No injury to my vehicle. Problems for the other automobile total up to about $900. I wont be spending a deductible and have liability  insurance  with USAA. My driving record has been clean . Can I just pay-out of wallet or document the claim with  insurance ?? The person who possessed the ruined car is really a friend and stated if I pay them right a state will not record