My 2 1/2 yr old son got a cold from my 9 yr old son about 2 weeks ago, and it eventually got mostly better, but now he has a pretty intense cough that sometimes makes him gag and he's grown up once from coughing so hard. he had fevers off and on from sund

Bronchitis: Likely a prolonged viral illness with bronchitis (RSV is common at this age). This may cause reactive airway disease (an asthma-like condition) which is best treated with expectorants (i.e., guafenesin), fluids and humidified mist treatments (hold him in a steam shower). If there is fever, increasing fatigue or poor appetite then see your MD to evaluate. Pertussis or whooping cough-not likely.