If your son has post-nasal drip from a chronically inflamed nose (be the cause irritant, allergen or infection), he could benefit from nasal irrigations and an inhaled steroid. The lack of demonstration of safety of oral antihistamines has not been established for children under age of 6 years.
There is, the possibility that the source of the mucous is asthma, rather than post-nasal drip and you do mention bronchial spasms. Granted, bronchial spasms can accompany harsh coughing but his doctor or a pediatric lung specialist (pulmonologist) should evaluate your son for asthma as treating it would be quite different from treating nasal inflammation. A final consideration would be that he has acid reflux and the irritation from it is generating the production of excess mucous.
Good luck