Re: Coughing when running around?
It sounds like it is lingering from his cold but could also have RAD (reactive airway disorder) My middle son has this. It is basically asthma, but before it can be technically diagnosed. Until he can take a PFT it isn't technically asthma.
Are you able to listen to his lungs when he is done running around? Just put your ear up to his back where his lungs are and listen as best you can. If you can hear anything other than him breathing I would get him seen.