I mean that doesn't surprise me--I know it doesn't sound like the vet was specific about the type of infection they're treating with the antibiotics, but whenever I see crusty eyes in any animal, my first thought is upper respiratory infection. If he has an upper respiratory infection, then sneezing makes a lot of sense, especially now that he has antibiotics helping him clear the gunk out of his system. And the rubbing his head on the perch could be him trying to rub the gunk out of his eye? Keep an eye on it of course, and if it gets worse let the vet know, but it really sounds like you're headed for recovery!
If he starts hanging out on the floor again, or if you can see he's struggling to breathe, those are signs to call the vet. When birds struggle to breathe they often stand oddly, with their tails kind of tipped downward and their wings hung low. This forum is always happy to look at pics, if you ever check on him and you're worried about him.