welcome to Healthcare Magic Forum,
He seems to be having allergic bronchitis
, which need not come from smoke alone. Cold weather or cold foods, any type of smoke or dust also can cause this. He must be getting exposed to some of these things regularly at home or places where he is which is preventing his cough
to improve. Make sure you take care of all those. A short course of steroid
should help but better it be prescribed by your pediatrician
. He will be fine.