My daughter got bit by an insect at a hotel in SC. She had to receive medical treatment because the site of the bite got infected. Do I have a case?

Most likely, you will need to hire an attorney in South Carolina.  Generally, a hotel can be found negligent if the hotel managers and employees knew or should have known about a dangerous condition and failed to take reasonable steps to protect guests from the hazard.   Insect infestation is a known problem in the hotel industry.  If your daughter had a serious injury, she may have a right to sue.