I wonder if they gave him something that upset his stomach? Being homesick wouldn't cause him to vomit up everything he tries to eat.
The general rule is to rest the tummy for about 12 hours. If you keep offering food, it will just come back up as you have found. After 12 hours, try a little boiled chicken breast and rice, just a spoonful at first. If that stays down, you can wait about a half an hour and try another spoonful.
If you have any Pepto Bismal on hand, that will help settle his stomach if he can keep it down. For his weight, he would get a 1/2 teaspoon every four hours as needed.
If he doesn't get better, please take him to your vet. I'd be worried about pancreatitis. Yorkies are prone to it.
Pancreatitis (Inflammation) in Dogs