If you’re hurt and the other driver is at fault, the answer is generally yes.

Anyone who has been in a car accident and has been hurt should seek medical attention, either at the emergency room, at an urgent care facility, or from a primary care doctor. Since you’ve been charged with those bills but didn’t do anything wrong, the general rule is that you have a right to be paid back for what you were charged, even if you were wise enough to have health insurance.