My Jack Russell coughs after playing and growling. Is it bad?

Occasional coughing in a young dog is not necessarily a cause of concern, just like occasional coughing in a person is not always problematic. As long as buddy is still eating, drinking, urinating, and defecating normally, I wouldn't worry terribly about what you are seeing. If he is playing and moving around with energy, it is unlikely that the coughing has anything to do with exercise intolerance or an underlying cardiorespiratory disease. This could not be ruled out however without some imaging at your veterinarian. Jack Russell Terriers can also be prone to having a collapsing trachea, a condition that can cause coughing during periods of excitement. Depending on the extent of the collapse, the coughing could become more frequent and more severe. This is another condition that could not be verified without x rays. I don't think that this is something that currently requires a veterinary visit, but I would mention it to the doctor at your next wellness visit.