Is it possible to have only vomiting but not other symptoms(not even diarrhea) for a stomach flu?

Initially, yes: Vomiting is a presenting symptom with intestinal viral illness, since it is often a secondary infection to respiratory viral illnesses, but with peristalsis and gravity to assist viral exposure, the lower GI tract eventually gets exposed and symptoms will progress to abdominal pain , cramping, and diarrhea, mucous in stool, and in severe cases GI bleeding