It is looking like mild gastritis or some gastric irritation as he vomited. You can give one dose of antiemetic like ondansetron
in a prescribed dosage and after half an hour you can give some amounts of cold milk if he asks.
Give sips of oral rehydrating solutions to prevent dehydration
If vomitings continue or any new symptoms like fever or loose motions develop then consult your Pediatrician
for further management.