I’m not familiar with screwworms but apparently they are as nasty as they sound (pdf):
Screwworms are fly larvae (maggots) that feed on living flesh. These parasites infest all mammals and, rarely, birds.
Female flies lay their eggs at the edges of wounds or on mucous membranes. When they hatch, the larvae enter the body, grow and feed, progressively enlarging the wound. Eventually, they drop to the ground to pupate and develop into adults. Screwworms can enter wounds as small as a tick bite. Left untreated, infestations can be fatal. Screwworms have been eradicated from some parts of the world, including the southern United States, but infested animals are occasionally imported into screwworm-free countries. These infestations must be recognized and treated promptly; if the larvae are allowed to leave the wound, they can introduce these parasites into the area.
Haiti is one of the countries where screwworms have not been eradicated. There is some concern that refugees coming to the U.S. from Haiti might bring pets infested with screwworms. The state of WA addressed this concern (veterinary inspections required for dogs coming from Haiti) but I could not find anything for South Carolina. I did come across a mention of the subject regarding FL but no specific policies or protocols are provided.
Bonus: Humans can host the larvae too! The pdf linked above has lots more gory details, if you are so inclined.