If your medical bills exceed the defendant's auto policy limit, the defendant is still legally liable for the full amount of your damages. You can seek compensation directly from them or from an umbrella insurance policy if they have one.
Also, if your medical bills still exceed the defendant's auto policy limits, you can look to your own uninsured and underinsured motorist policy, or your health insurance. You can negotiate to settle your medical bills from the funds that you receive from the defendant's insurance.