My 4 months old has occasional inspiratory wheezing after eating what could it be?

Reflux or infection: Inspiratory wheezing usually means obstruction high up in the airway. A foreign body is possible. Croup and epiglottis can do that but it would not be occasional. Asthma causes expiratory wheezes and he is a little young for that. Bronchiolitis usually causes expiratory wheezes as well. Pertussis can cause an inspiratory whoop that may sound like a wheeze. Reflux must be considered.

Swallowing study: I agree that there are a number of possibilities. In addition to anatomic narrowing of the airway which is worsened during eating, I would also consider aspiration of mouth or gastric contents. A retained foreign body in the airway is also possible. Your physician may order a swallowing study in conjunction with speech therapy.