Visserion, I think you might be misunderstanding something crucial if I'm reading correctly. The white/long-tube
UVB bulb produces no heat, it provides radiation. The basking spot people are talking about is under the OTHER bulb, that one that produces the heat. (EDIT: he also need's to be within 6-8inches of the UVB tube bulb as well. Didn't make that clear.)
You need to give him something he can climb onto so he is 6-8 inches from that hot basking bulb (the hammock should work). He should be spending most of his time chilling on a hammock/rock/log 6-8inches under that hot bulb. Then, you need to measure the temperature there, with a $10 temperature gun from Walmart/HomeDepot/Lowes. The dial thermometers are highly inaccurate.
Bearded Dragons use high heat to digest food, they are from the austrailian outback. He is not getting hot enough, which is why he isn't digesting the worms properly.
He also probably isn't
hydrated enough unless he's eating ALL those misted greens, but it sounds like he probably isn't eating them all because he isn't feeling too good. Until he is better, I recommend putting him in the bathtub or sink with a couple inches of LUKEWARM (not hot) water for 10-15min daily. At a minimum right now be doing that every other day. This will aid digestion. Just let him sit there in it. Remember more
hydration does NOT equal more humidity, which I'll get to next:
Stop misting the greens. The humidity in that glass tank is probably way too high if you're misting inside the tank. Beardies need it very dry (30-40% humidity). Let him get all his water from the bathtub/sink, from the worm's guts, and the insides of his veggies, you really don't need to mist them. The humidity probably gave him an upper respiratory infection (URI) which is why the vet gave him antibiotics, think of it like beardie bronchitis.
EDIT: I recommend removing the water dish as well, or getting a much smaller one. If that's a hygrometer (humidity dial) on the back, it looks to me in the picture that your humidity is above 60%, which is way too high. I can't see it clearly.
For the mealworms that are causing impaction, I understand meal worms are easier for you because you can't have roaches, crickets, etc. Superworms and phoenix worms are just as easy to have, just as clean and way more nutritious. Your beardie is old enough to eat them. They are pretty inexpensive too, and stupid easy to breed if you want to. There are numerous guides on this site as well as others online on breeding them. I bred them myself, and you don't really have to do much. Once it gets going, you also won't have to buy worms ever again. My main point is you should get off mealworms in any way possible, the chitin shell they have screws up your beardies stomach.
If you change the basking spot, the
hydration, and the worms to a different worm how I've laid out here, I'm sure he'll make a full recovery. If he doesn't, it could be something more serious, but I think it's unlikely considering he saw a veterinarian and got antibiotics. Could also be that the veterinarian wasn't aware of the stuff that was wrong with his tank and food, or just didn't care.