Is it a dry, non-productive cough (non-productive cough does not expel any mucus)? If it is, then it might be a cough-variant asthma. Cough-variant asthma is sometimes called chronic cough to describe a cough that has lasted longer than six to eight weeks. It is common in kids with "childhood asthma", just like what you've said. You should recall if you were exposed to allergens, or breathing in cold air because coughing may start from those. I suggest that you set an appointment with an Allergist or Pulmonologist (asthma specialists).