A friend whose child had respiratory issues could not be held by someone who had been smoking (i.e. the person needed to change their clothing first -- depending how much they smoke and how great his sensitivity a shower might be needed to get hair clean), could not go to a house where there was smoking -- not that anyone smoked around the child, but she could not tolerate smoke residue -- until your son gets fully over all of his respiratory issues; I'd follow those same rules.
You're right to worry about Asthma, but they won't be able to diagnose until after he is over the Bronchitis. To prevent his getting Asthma, I would be really strict about the smoke issue while he is healing. Also, because he shows the sensitivity; you might want to work with your parents going forward to minimize exposure.