1) what color was the vomit 2) are the beak and legs pale 3) has it been free ranging 3) were there any worms in the vomit 4) what do you feed it? Have you given anything new today? 5) whats the temp like by you ? 6) how old is the goose ?
Also I would not freak out about diarrhea. The digestive system of poultry is no where near that of humans , they don't have "diarrhea" . With a wide range of normal poops water stools is normal with the summer heat and the increased water intake.
Doesn't sound good. If you can afford (or even have one near you) an avian vet I would think that would be a good option. Or just make him as comfortable as possible and make sure he's eating and drinking and maybe give some electrolytes and Vitamin B.