The only thing that you can do for him at home is go ahead and switch him over to a bland diet of only boiled chicken and white rice or cottage cheese. Most dogs will eat this and it sits well on the stomach. It will help with the vomiting an diarrhea.
I would also add some plain pedialyte to his diet to help replace the fluids that he's losing through the diarrhea.
If this does not start to resolve with this method, you will want to see your vet.
Let me know if you need more help.
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