My dog is throwing up bile and won't eat. What food helps his upset stomach?

Honestly we rarely have to put these dogs on a special diet but if I had to pick a diet I would say high fiber which may help with GI motility. A prescription diet from your vet like Hill's w/d would be best. I would use the canned version.

I am a bit worried that the diagnosis is not correct. There are many other reasons why a dog could be vomiting bile (parasites, partial GI obstruction, GI motility disorder, cancer, endocrine disorder, food intolerance/allergy, etc). Did he have any blood testing done? X-rays? I think you have already done what should be tried for simple bilious vomiting syndrome. Since he hans't improved and is actually worse, I strongly recommend you consult with your vet about more testing. I am also concerned as this is a diagnosis usually seen in older dogs; Earl is young to have this issue.

In the meantime you can try giving him some over the counter antacid (famotidine) 10mg once a day but only give this until you can get him back to your vet.

( https://www.walmart.com/ip/Equate-Maximum-Strength-Acid-Reducer-Famotidine-Tablets-20mg-200-Ct/24360533 )

Hope this helps. Best wishes.