Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that you are concerned about Loki not eating well and vomiting after his neuter surgery Tuesday.
He may have eaten well the first day because pain medications given before and after surgery lingered and he couldn't feel his sore throat.
It is not uncommon to have a sore throat after anesthesia. This can be related to the endotracheal tube we use to administer oxygen and anesthesia, or it can be related to a dried out throat when anesthetized or finally many animals under anesthesia will experience gastroesophageal reflux, and stomach acid burns the esophagus and throat horribly.
The more he vomits, the more his stomach acid will affect his throat, so ideally we need to get him to stop.
At home to 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, are very safe, and should help him feel better by decreasing acid production and this decrease acid burn/reflux. They can be used as needed.
The gut slows down with the effects of the anesthetics and dehydration, and if his ingesta isn't moving he won't feel hungry.
You can try a soft, bland diet with increased fiber to perk his appetite, feel better on his throat, and get his gut moving. A homemade diet for this is 2/3 boiled white, skinless chicken, all fats drained off the meat, and 1/3 boiled, white rice. Add 1 to 2 tablespoons of canned pumpkin, (not pie filling, just pumpkin), to each meal for fiber and low salt chicken broth to his meals as well to get more fluids in which should help as well. The softer the food the easier to swallow, and the more enticing it is.
Once he is back to eating well and passing stools you can slowly convert him back by mixing in his regular food, adding a little more regular and less bland at each meal. It should take a week to get him converted back to regular food.
At this point I would not be too alarmed. If he isn't improving over the next 24 hours though he should be rechecked.
Best of luck with your fellow, please let me know if you have any further questions.