Sometimes when I'm REALLY paranoid, I see what looks like a scale (or two or three) sticking out. Not sure on "shedding", might want to ask someone else on that. It's never gotten to the dropsy stage, so it might just be the paranoia.
Okay, since you're getting a bigger one, I think it's best to be patient and see how he takes the bigger space (how big?). However, if you really see him sicker (color fading, he's really not swimming, he lays at the bottom and swims very, very slowly, lethargy, not eating - any of these symptoms consistent doesn't have to be all ) then take bigger action.
I'm skeptical about the Betta Revive, but I've never used it before and I'm not sure what to think about it. Again, I don't like the thought of any additives in my tank. Go ahead and keep using it and if he doesn't seem better (and you're doing water changes and whatnot), then try changing conditioner, just as experimentation.