My baby was throwing up every formula bottle he ate for three days and now he is coughing until he throws up and has a stuffy nose. no fever?

Vomiting : This could be associated to a viral syndrome which is very common. However depending on the baby's age if he is in his first 2 months of life and gets fever that requires immediate ed evaluation. In any case the fact that he has been not tolerating anything for 3 days deserves for him to get evaluated asap. In the meantime trying small sips of pedialyte can prevent dehydration.