You said that the first vet did a skin scraping...What was the result? Did he tell you why he was prescribing an antibiotic? What antibiotic(s) was he given, and how long was he on them? Did either of the vets you have seen suggest it may be a fungal infection? Viral? I'm confused as to why the first vet actually did a skin scraping, which is the first test that should have been run, and then put him on an antibiotic without explaining why. Obviously an antibiotic would only treat a bacterial infection, not a fungal infection, viral infection, parasite, etc. Any vet would know this, so I'm wondering if he found bacteria in the skin scraping and if so, what bacteria it was. If he wasn't a certified Reptile vet with bearded dragon experience, it's possible that he saw normal bacteria that all bearded dragons carry on their skin and prescribed a broad-spectrum antibiotic to try to kill it, which would not only not help the lesions but may also kill off normal, good bacteria and upset his system.
I think the first thing you need to do is find a Board-Certified Reptile Vet with a lot of bearded dragon experience, there has to be at least one really good certified Reptile vet in the greater Miami/Fort Lauderdale area. I'd do a search online for a very good reptile vet, look at credentials and ratings, and then call and ask questions about their bearded dragon experience. And make sure to tell them that this has been progressively getting worse over weeks and months, that he's seen 2 other vets, been given antibiotics, and it's getting worse and worse. They hopefully will get him in quickly that way. And if you never got the results of the skin scraping that the first vet did you need to call them ASAP, get a copy of the test results, and ask specifically why he was put on the antibiotic he was given. Don't ever be afraid to ask questions, and ALWAYS get a copy of all test results, his complete chart with notes on his diagnosis, etc.
In the meantime you need to completely sanitize his enclosure and everything in it. Throw out all rocks, wood, etc. that is porous. You need to order or find some F10 (bleach will work in the meantime) to disinfect his enclosure, both inside and out. Use only disposable substrates from now on like paper towels, and change them often. You need to soak his enclosure in a mixture of the F10 or bleach and hot water, rinse well, then dry well. Even the stand his enclosure is on. And keep all other animals away.
As for him, no more baths, if it is a fungal infection then dampness will spread it. What you can try while waiting to get into the certified Reptile vet is buying either Betadine (iodine) or Hibiclens at Walmart, along with a few gallons of sterile water. Mix the Betadine or Hibiclens with the sterile water, like 1 part antiseptic to 2-3 parts water, then heat it until warm but not hot (don't want to burn him). If using Betadine the solution will look like a weak iced tea, the Hibiclens is pink, so the solution will be very faintly pink with some soap bubbles. Both are great antiseptics that are used in the scrub packs in hospital operating rooms and they kill everything. Soak him in this warmed solution for 15-20 minutes twice a day, then dry him really well. Then also buy a topical antifungal medication at Walmart (or any drug store, I find Walmart cheaper), I'd start with Lotrimin or the generic Walmart or store brand of Lotrimin. It's a pretty broad-spectrum antifungal cream. Apply it sparingly to each lesion, just enough to cover each lesion and rub it in as well as you can. I'd do the antiseptic soaks and apply the topical antifungal cream twice a day. Other than these treatments keep both your bearded dragon and his enclosure completely dry at all times. Clean and dry is going to be very important for both him and his enclosure and anything he touches. Also keeping his basking temperature high enough but still having a temperature gradient from a cool side between 75-80 degrees so he can get out of the heat is important.
Keep in mind that the soaks in the antiseptic and the topical antifungal cream are only meant to try and slow the progression of the fungal infection, but only If it's a fungal infection! The Betadine or Hibiclens soaks will kill both bacteria and fungi, but they won't "cure" him, only slow the external, topical infection if it's bacterial or fungal. If it's a viral infection that he has then none of this will do much of anything except keeping the external lesions from developing infections secondary to the actual disease that's causing them. The only way you're going to cure this is to take him to a certified Reptile vet ASAP, get the cause of the lesions diagnosed, and treat the Infection with aggressive medications. I'm hoping it's not Yellow Fungus, it doesn't present like Yellow Fungus in the typical fashion, but that really doesn't mean anything. What most people don't understand about fungal infections is that they are growing both internally and externally, but all we can see are the external representations of the infection. So a lot of people will try to get away with treating Yellow Fungus with only topical creams, while the fungal infection is raging internally. So it's vital that you get him to a certified Reptile vet who will run the appropriate tests to diagnose and then treat him.