shelleycat
you poor thing! going thru a dog's passing and now an ill dog...
dogs from shelters do go through an adjustment period of a month to three months. Sometimes the vomiting is due to shots, change in food, stress, or all of the above!
Are you feeding him a high-quality kibble such as Innova or Wellness? The worst mistake anyone can do is to feed a dog pet food from a grocery food. Real food, table scraps even, is SO much better.
He needs very simple food right now. Cook up some chickena nd break it up for him, and cook up some quaker oatmeal - no milk, but go ahead and dress it up with butter, olive oil and even some brown sugar. Dogs like things that taste good just as much as we do. Plus he'll be a bit dehydrated and needs foods that are wet, not dry. Kibble is exactly like eating raw pasta. Blech!
You can also find doggie pepto-bismal at the pet stores and even health food stores. I'd do that before taking him to a vet. I'm not an alarmist and don't take mine to the vet unless there are other symptoms or the vomiting persists for more than 3 days after change in food.