To prove hydrogen sulfide a hapten, its conjugation to a carrier molecule followed by induction of H2S-specific antibody would be required. I am not aware of any such study. I do not think that sneezing caused by inhalation of hazardous gases should be taken as a sign of allergy.
It is highly improbable hydrogen sulphide may be work as an hapten because it is very unstable, poisonous, corrosive, flammable, and explosive. In my opinion, probably an irritant mechanism on bronchial muosa is more likely to induce bronchospasm