I would take him to the vet if your medication doesn't do any more good than it has so far. It does sound like some kind of allergy reaction but to what is the question. It could be something as nasty as a fire ant bite - Florida is notorious for fire ants and they can appear and disappear just as fast! Not trying to scare you but it is one of the problems with the area
Hope your furbaby is feeling great soon and you can all enjoy your new home without any more welts
