My first impression of the find is that it is an otolith - a bone from the inner ear of a fish. A large one like this is most likely to come from a Sciaenid species aka the drum family. Considering the location, a red drum would be my first guess. There are three bones in the inner ear on each side of the fish's head, called the saggitus, lapillus, and asteriscus. I think you may have a sagittus or lapillus from a red drum.
There are freshwater drum species as well and they also have large otoliths and they are commonly found on beaches after the rest of the fish has decomposed.
I have seen otoliths drilled and made into earrings. They are commonly used in fisheries science to determine the age of the fish. The otolith is dissected out and is either embedded in epoxy and cut, or sanded/ground until a thin cross section can be viewed on a microscope. You can do this with larval fish to look for daily growth rings (I've prepared slides of these and examined them by the hundreds of thousands) or older fish in temperate zones to see annual growth rings - just like tree rings.