C.M.
We have had this problem with our 2 year old basically all winter. She hasn't had the stuffy nose as much but has had the cough, mostly at night and in the morning, off and on for a long time. I ask my doctor about it just last week and he suggested starting her on Claritin. The have a childrens formula and you can also get it in the generic brand. Yes the humidifier will also help. We started one in our girls room a couple weeks ago and it has helped with the cough but not eliminated it. I would say treat it as allergies, especially if dad has them. We are getting into major allergy season so it will probably only get worse.