My son, 4yrs old is having recurrent cough and his skin is itchy dry and patchy. What could be the reason and available treatment options?

Likely unrelated. Itchy dry skin can improve using any moisturizing agent like Gold Bond lotion or whatever similar product you have in your country. Recurrent cough can be related to too many issues to cover in a simple answer.The first issue I would address is any exposure to fumes/smoke/fragrances/dust and similar irritants that can trigger cough in anyone.Reducing such exposures is a good first step.