My 3 month old son has a dry cough he vomits after meal what would be the cause?

Several things: The first months are troubled by narrow nasal passages &exposure to dust, fragrances, smoke & other irritants.Baby tries to flush these out of the nose with mucous but this often ends as congestion & produces cough.Cough can trigger vomiting at that age. The best rx is washing out the nose with saline &suctioning the remainder. Eliminate irritants from babies environment & this will happen less.