Hello there I have read through your question and understand your concern. Persistent cough with low grade fever points towards a diagnosis of upper respiratory tract infection. The vomitting may be due to excessive coughing. I would advise you to take him to a physician and consider getting his Chest X Ray done. Also a physician can auscultate his chest to determine whether there is any congestion. If the cough persists or there is expectoration then he may require a course of antibiotics. Nebulization will also help to relieve his congestion. I hope that answers your question. If you have any further questions please feel free to write. Thank you for choosing healthcare magic.