He's about 5 inches? I think he'll be just fine in the 20 gal until he recuperates. Just keep up with your water testing to make sure ammonia/nitrite/nitrates don't get out of control. I think that would be the biggest problem with keeping a medium-large fish in a smaller tank. Except, of course, that he may be lonely for his buddies. But you're absolutely right, it's best to keep him separate until you can be certain that he is better. Plus, it will help you spot-feed him (without the other fish grabbing the food first) to get his strength back up.
For the sores, I'd say try some Melafix. There's some question as to whether Melafix actually does anything, but it's all natural so probably can't hurt. Anyway, it's going to be preferable to anything chemical that might send him over the edge in his weakened state. Just make sure to increase surface agitation or add an airstone, as Melafix tends to make the water thick and slimy and therefore decrease the amount of dissolved oxygen.
For an appetite stimulant, you could try soaking your regular food with a piece of sliced garlic. Just throw in the garlic with some tank water and the food for 10-15 minutes. I haven't done this one yet, but have heard it's a great way to encourage finicky or ill fish to accept food. Or maybe give him a treat he normally doesn't refuse like brine shrimp. At this point, it's important to get something, anything in him to give him energy. He's going to need it
Again, congrats on his turnaround and I'm still crossing my fingers for you.