If you want to give a kitchen Herb a try Thyme might help relieve the cough. Boil a couple of heaping tablespoons or so of Thyme in water for just about a minute and turn off the burner and let it sit (to make a tea) Have him sip this, it should help with the cough.
As far as his Asthma, parasites in the lungs comes to mind, especially because you say he is allergic to many things. But don't bother asking the doctors about it because they are not trained to tell you this.
Try the Zapper Forum as a start, and the Rife Forum here if you don't want to go the route of Herbs.