If you can prove with admissible evidence that another vehicle caused your damages then you can file a claim with your own Uninsured Motorist policy. Some evidence to obtain would be the accident report, photos of your vehicle and paint chips left by the other vehicle. These will help you prove that another car caused the accident. Also, you and the passenger must treat for your injuries soon or the claim will be denied.
Given that you have a witness, the John Doe requirements are satisfied if they corroborate your story and you could make a claim and eventually file suit against your own Uninsured Motorist coverage for your injuries. I would make an immediate appointment with your family doctor an urgent care clinic and follow their advice on further care because gaps in care, even if well intentioned can be deadly to a case. Below is a link to my post on Georgia Hit and Run issues.
As far as your friend is concerned, if he disagrees with you and contends that you caused the crash, then yes he might claim against your insurance company. That would also destroy your ability to make a claim for injury.
Sign up to receive a 3-part series of useful information and advice about personal injury law.