You stated that you have full coverage so that means that you should be able to place your claim for the damages to your vehicle from the hit and run accident under your Collision portion of your physical damage coverages. Whether you will be reimbursed for a rental car as well or other expenses depends upon the rest of your car insurance coverages.

If the other party in the hit and run was found and has insurance coverage than you can place a claim for your damages and expenses through the driver's Liability (Property Damage and Bodily Injury) coverages. If the person is uninsured or not found than you will need to go through your own insurance depending upon your coverages.

If you have rental car reimbursement as part of your coverages you should be able to use that for use of a rental car while your car is being repaired. As for your medical bills and associated expenses you would need to have coverages such as Personal Injury Protection (PIP), Medical Payments (MedPay) or Uninsured Motorist Bodily Injury (UM) to cover you.

To see what benefits you can get from your car insurance policy for your injuries and damages read through your policy and speak to your insurance agent. If it turns out your auto insurance does not cover your medical expenses stemming from the accident you can see if your personal health insurance will pay. If this is not an option and the at-fault party is identified you may need to take them to court and seek a judgment against them for the monies you are out due to the damages and injuries you sustained in the accident.