If my child's friend is injured in my back yard, can the parents sue me for medical bills? If so do I have any protection under my homeowners policy?

You have 2 layers of protection with your NC homeowners policy.  The first is a coverage called medical payments coverage which can pay for the medical bills, up to the limits of med pay on your policy without any regard to who is at fault.  To trigger this coverage the injury just needs to have happened on your property to someone who is not a resident of your home.  If you are found at fault for the child's injuries then your liability coverage on your homeowners policy can protect you.