My son and daughter both have this problem when they go out and play and run around they start coughing like crazy after what could this be?

Exercise cough: Two things come to mind. First would be environmental induced allergies. Does this occur year round when they're running around or just spring/summer or just autumn. Then I'd suspect a pollen causing allergic symptoms. More likely, though, especially if year round, is exercise induced asthma. There is a subset of asthmatic kids that ONLY have symptoms when they exercise. This is very treatable!

Allergies,asthma: Could be allergies to environmental agents.could also be exercise induced asthma.talk to your pediatrician about this.