Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your fellow isn't feeling well and is eating poorly and has vomited 3 times since yesterday. I am glad to hear that he feels well enough to remain social.
Vomiting and a change in appetite can be related to eating something he should not have, too many treats or table food, eating foreign material (which could cause a full or partial gastrointestinal obstruction), chronic pancreatitis, a dietary allergy or sensitivity, toxin exposure, a viral or bacterial infection, inflammatory bowel disease, heartworm disease, hyperthyroidism (a tumor of the thyroid gland) with internal organ damage, organ failure, or even infiltrative cancers such as lymphoma.
Because he hasn't eaten normally in several days and he is vomiting I am very concerned about him. If he isn't drinking well either he will quickly become dehydrated, especially because he is vomiting as well, and as his liver breaks down fats for energy to live he may develop a type of liver disease called hepatic lipidosis.
Ideally he would see a veterinarian today if this has been going on for more than 72 hours. Simple stomach upset should pass within 24 to 48 hours. They could examine him, run blood tests and possibly check radiographs and/or an ultrasound to evaluate him and know best how to treat him.
In the meantime they can administer injectable anti-nausea drugs and fluids to rehydrate him.
If you cannot have him seen for whatever reason there are some things you can try at home.
At home to try and settle his stomach you can give either:
1) Pepcid ac (famotidine) at a dose of ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours
These are acid reducers and may help him feel less nauseous so that he will eat and hopefully not vomit. They are quite safe and can be used for several days if necessary.
You can use a medicine syringe to try and force water or broth into him orally if he hasn't been drinking.
A couple of hours after giving the acid reducer I recommend offering meat baby foods or a bland diet of 2/3 boiled minced white skinless chicken and 1/3 boiled white rice mixed with some low salt chicken broth to make it more palatable and get additional fluids into him.
If he continues to not eat he should see his veterinarian for an examination, diagnostics and intravenous fluids and supportive care.
Please let me know if you have any further questions.