There are three possibilities here. First, your health insurance company should pay the bills, even though they are the result of an automobile accident. In addition, your driver’s automobile insurance policy (or your policy if you were the driver) may have coverage for medical bills, usually up to $5,000. This is called medical payments coverage and is part of most full coverage policies. These payments can be made as soon as the medical expenses are incurred. Finally, the other driver’s auto policy is responsible for your bills if the accident was his fault. You will not see the money from the responsible party’s insurance company until the final settlement is made, but compensation for the full price of the medical bills is part of the settlement.