Bacterial or viral lung infection can precipitate asthma with wheezing in a person genetically predisposed to asthma.
Treatment of the presumed asthma, aside from
treatment of the infectious
pneumonia, is appropriate. So, this could be asthma, superimposed on pneumonia.
Your son could have whooping cough, despite immunization against it.
If his fever and sweating with clammy skin has subsided, it is probably a sign that the antibiotic therapy has been effective and the pneumonia is clearing.