Hello! As you remember, "queasy" means "likely to vomit", so, I think, as luck would have it, the speaker's smile looks as if he's going to be sick. It doesn't mean that people would follow suit and feel nauseous, my guess is that smile simply looks unattractive ( or so the speaker thinks).

'Queasy' always means 'feeling sick', so the suggestion is that it is a smile that makes people feel sick when they see it. It's a slightly strange sentence though. Although there are a few smiles that would make people feel sick, I think it would be odd for someone to describe their own smile as that. Perhaps they have very rotten teeth, or a facial injury?