Can you receive compensation for injury sustained at a resort in Antigua?

The answer is maybe. Some resorts in the islands have forum selection clauses in their hotel booking information when you purchase and reserve accommodations. You would need to review all the contractual itinerary for your hotel reservation etc. to see if in fact they allow a resident guest of the United States to file suit in the US court arising out of an injury occurring on their property. If they do, it's almost exclusively that they will select courts in the state of Florida. However this is all speculation until you have counsel review all your travel itinerary documents regarding your resort reservation. The other issue is liability. There is no strict liability for any injury that happens on any property. You're going to have to prove that they were negligent and that negligence caused your injury. It is not clear from your fact pattern how they were negligent.