Parvovirus gastroenterites is a huge concern, but if he was properly vaccinated as a puppy with a series of 3 to 4 vaccinations from his vet at 3 weeks intervals, then this is not likely at all. If he is not vaccinated, then your vet can do an easy in house test to screen. Usually this virus causes profound bloody diarrhea and vomiting. The vaccine is extremely effective. Now, there are other viral conditions, such as coronavirus that could cause similar signs. There are also other issues that could cause vomit/diarrhea such as you are seeing such as pancreatitis, liver issues, kidney issues, intestinal parasites, an endocrine problem such as Addison's disease, and the list continues.
Sounds like the next best step would be some lab testing. You can discuss his risk for parvo and if it is worth running this test. If he was vaccinated properly, then I think this not necessary but would spend money on a CBC and chemistry profile +/- stool check (if he is on his monthly heart worm preventive then unlikely to be parasites unless on one that doesn't cover whipworms and this could be whipworms).
Great that he is on the i/d diet. This can only help. Also having him on a daily probiotic can be useful. Sounds like, though, he needs more than this sort of supportive care and may need more prescription medication for his symptoms such as something to stop the diarrhea (like metronidazole) and something for ongoing nausea beyond what the injection could cover (only works for 24 hours).
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