I don’t think zoas Pack much of a punch in reference to stings, but I reserve the right to be wrong. (I’m saying that a lot lately.) My clowns were getting stung by my euphylia and it was causing them to have a clear spot (not white, but clear. They were see through at the stings.) but that stopped once they were acclimated to them. I don’t remember any heavy breathing.
I would think if he was struggling for oxygen he’d also be gasping at the surface. I know clown fish can be weird sometimes. Hopefully it just ends up being your clown’s brand of weirdness. I’m also following along to read what other advice people have to offer.