Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Roxy is vomiting yellow, bile material and isn't eating or drinking for the past 3 days.
Yellow in the vomit means that the small intestine is refluxing bile into the stomach so that when she vomits you see the yellow color. That isn't normal as bile doesn't belong in the stomach, and it does mean that there is some reverse motility, but it isn't specific for any particular disease process.
In many cases vomiting is triggered by eating something they should not, too much table food, too many treats or something they find outdoors, esophageal reflux, or a dietary allergy or sensitivity.
More serious causes of vomiting include viral or bacterial infections, chronic pancreatitis, inflammatory bowel disease, internal organ failure (kidney or liver disease), a full or partial gastrointestinal obstruction or even infiltrative cancers such as lymphoma.
Because this has been going on for 3 days she is likely very dehydrated so ideally she should see a veterinarian today.
If that is not possible for whatever reason to ease nausea it may also be helpful to put her on an acid reducing medication as too much stomach acid is very irritating and predisposes to vomiting.
I recommend giving her a dose based upon her weight. You can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours
These are both acid reducers and may help her feel better. They are quite safe and can be used for several days if necessary.
I would not feed him any food for 12 hours after the acid reducers are started. This should help stop gut spasms and restore normal gut motility. Small amounts of water or ice cubes given frequently are fine as she needs fluids after all that she has lost with vomiting. You can give her pedialyte to drink in small amounts a couple hours after one of the acid reducers is given to replace fluids and electrolytes.
After her food fast start a bland diet of 1/3 boiled, lean hamburger (or boiled, white skinless chicken), all fats and juices drained off the cooked meat, mixed with 2/3 boiled, plain white rice. Feed several small meals a day.
Once she feels better (no vomiting for 48 hours) start mixing in her regular dog food very slowly. Less bland more regular with each day. It should take a week or so to convert her back.
But if she continues to vomit even with the acid reducers and bland diet, runs a fever (more than 103F rectally), has a tense painful belly or if she refuses to eat even with the acid reducer being given she should see a veterinarian for an examination, and some diagnostic testing. I would start with a complete blood count and biochemistry profile, a specific test for pancreatitis called canine specific pancreatic lipase, as well as fecal checks for parasites.
Please let me know if you have other details or a particular question based upon my response.