My tentative answer is that it is real. Clean it up with some muriatic acid and then post an update with pictures.
When you say you found it near the sea wall, I presume you mean the hardened shore wall on St. Augustine Beach (pier area). I can't fathom that you were in the muck of the sea wall in downtown without drawing suspicion. Not to mention the current location of the sea wall in downtown is not where it was even back in the '50s. If it is indeed the location on St. Augustine Beach, then it is likely as a result of being deposited after the renourished sand was washed out. Back in 2007, it was much lower than it is now. The beach was renourished to such an extent that the rocks in front of the sea wall was completely buried and level with the sea wall extending out to the water's edge by at least 60 yards. Of course, the renourishment has been eroding for the past couple of years with large volume of sand movement as a result of Matthew(2016) and Irma(2017).