So I take it you and your son both feel better when you're not in your home? That's usually a pretty good indication that your have a sick home. You replaced all your carpeting in your house or just some? Could that new carpeting be outgassing and causing your coughing? Because I have allergies to molds plus chemical sensitivities.
You might look around the house for anything new you bought just before you started coughing. Because the fabrics these days have terrible odors that cannot be washed out. Just a thought.