No — liability coverage pays for injuries and damage you cause to others. Your own injuries are covered by different sources: the at-fault driver's liability coverage, your own medical payments (med-pay) coverage, your uninsured/underinsured motorist coverage, and your health insurance.

This is the gap that surprises people: if the driver who hit you carries minimum limits and you don't have UM/UIM or med-pay, your options narrow fast. It is also why reviewing your own policy is part of protecting yourself.