It matters what state you are in and your policy declarations, so you have to refer to your policy for specific coverage definitions. But uninsured and underinsured motorist coverage typically will compensate you for not only the out-of-pocket expense of your injuries, but for your pain and suffering as well.
Underinsured Motorist Bodily Injury covers you, the insured members of your household and your passengers for injuries, damages or death caused by the negligence of a person with insufficient insurance. If you have an accident with a person whose coverage cannot meet your damages, your policy will meet the difference-up to the limit of liability listed on your policy.
Uninsured Motorist Bodily Injury covers you, the insured members of your household and your passengers for bodily/personal injuries, damages or death caused by an at-fault uninsured or hit-and-run driver. If you are involved in an accident where the other driver is at fault but has no insurance, your policy will cover your medical expenses, up to the limit on your policy.