A., as I understand it, viruses usually run their course in adults in about 1-2 weeks, and for small kids it is doubled, so 2-4 weeks.
Last winter my two kids had some type of stomach flu, our 1 yr old daughter was better in about 1-2 weeks, but our son, who was 2.5 yrs at the time, just couldn’t seem to get over it. He’d be sick and vomiting, then he’d feel better and be starving, so he’d beg for milk. I’d give him milk and he’d start vomiting again. In retrospect, I realized that I was giving him dairy products too soon. Finally, when he felt better and was hungry, I did not give him anything that could irritate his digestive system for 2 additional days once the vomiting stopped. After that he was fine.
So, as the other mom’s have said, definitely get a second opinion. In the meantime, perhaps try only watered down juice and crackers/pasta for a couple of days after the symptoms cease to see if the digestive system needs some time to recover.
Good luck