This is a classic picture of a viral infection and infants can have vomiting
and loose motions with flu like symptoms. The treatment is simple. No antibiotics are needed. To check vomiting, you may give 1.5 Ml of Domperidone
drops 8 hourly and give tylenol for fever, only after the vomiting subsides. Give your baby plenty of ORS like Wallyte/Zintrol/Peditral say about 3-5 glasses in 24 hours depending upon frequency of loose motions.
However if the vomiting continues then visit a Pediatrician
who may evaluate him for dehydration
and manage accordingly.