You can sue for medical expenses even if you have insurance to cover your costs. The Commonwealth of Kentucky does not punish people for getting health insurance. This means you can claim your total medical expenses at trial. Your insurance company will have a lien on the recovery for what they paid out on your behalf. The lawyer you hire may be able to negotiate the lien depending on policy language and the recovery. A jury will never hear that you have insurance nor will they hear about the insurance of the at fault party.