Yellow Fungus and Yellow Skin Disease are the same thing, some people will just call them different names. The fungus is a common fungus found in the soil and in places where things like leaves and grasses are decomposing. It's unknown why reptiles seem to have no natural immunity to it. It's thought that they can come into contact with the fungus, but it will only affect them if stressed, resulting in a suppressed immune system, or have some sort of open wound. The fungus' ideal temperature range is in the same range as the bearded dragon's so it's easy to see why the fungus loves them. It also produces dense colonies that can reach a diameter of 1.2 inches in only 14 days, which is why time is always of the essence in these cases. The fungus displays an optimum growth at 86 degrees F, so it will spread quickly once in the enclosure or present on the dragon.
Whatever it is, it could be a good idea to do a thorough cleaning of his tank so he doesn't re-infect himself while trying to heal. Bake any decor possible (i.e. don't bake silk plants, but things like wood, rocks, bowls, etc should be fine) at around 200 degrees for half an hour and throw out anything you can't thoroughly clean. Wash any fabrics in hot water, and if available, steam clean the empty tank. If you don't have a steamer, you can wash with a diluted bleach solution (I think 1 cup bleach to 1 gallon water), wash inside and out of the tank, let sit for 30 mins, then rinse rinse rinse. It would probably be good to let the tank air out for a day or two. Also, if you have a floor heater, furnace, or fireplace, you could set the tank infront of it, rotating it, so the glass gets hot enough to kill any left over fungus and also will help any bleach residue evaporate. His substrate (flooring) should be something easily cleanable, like paper towels, newspaper, or tile. I prefer tile because it acts as a complete barrier between the glass on the bottom and the poop and it's easy to steam clean/bake to properly disinfect.
If he does have YF, many times it is spread because the yeast and fungus pass through the system and they poop it out, then when the step on the poop, it spreads it around. This is why it usually appears around vents. So any poop should be moved immediately.
Iodine or Betadine baths could be helpful. If your baby likes to drink his
bath water, give him a fresh water
bath first, let him drink, then drain and refill. Add enough of the Betadine or Iodine to the water to look like weak tea and let him soak for a bit. Usually 10-15 mins, but if he likes baths, you can do 30.
A probiotic would be great, as a week immune system only makes the fungus stronger, but nothing dairy as they can't digest it.
The main point I want to stress is any little thing you can do at home will not be a cure. It could potentially help, and of course it's a good idea to try anything you can, but an oral anti fungal is needed to attempt to treat Yellow Fungus. Topical treatment will never cure it, if it is Yellow Fungus. And always make sure to keep a close eye. The fungus likes to play dormant and then spring up again, so even if it looks like it's going away, don't let it fool you.