Hello, my name isXXXXX and I have over 20 years of experience as a veterinarian. I am sorry to hear that Oliver is having diarrhea when eating wet food and is vomiting when eating dry food.
Vomiting and loose stools can be due to stress, a change in diet, getting into and eating something he should not have, parasites, a viral or bacterial infection, inflammatory bowel disease or even a food allergy. But they can also be related to metabolic organ disease (such kidney or liver disease) due to organ wastes irritating the gut. Rarely a mass in the intestinal tract can be the cause.
Because he is a younger cat, a food allergy or sensitivity, parasites, or inflammatory bowel disease seem most likely. While all cats vomit here consistent vomiting and loose stools are not normal and signifies an underlying problem.
If he is feeling well I am less concerned. He should be checked by his regular veterinarian if he's not bouncing back quickly with home therapy though. Well worth checking at least a couple fresh stool samples too as parasite eggs/cysts are shed intermittantly.They may be picked up on the second sample or third test if the first is negative.
If he still feels well now though we can try some things at home. To try and settle his stomach today you can try either:
1) Pepcid-ac (famotidine) at one 1quarter of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours.
These will reduce stomach acid and should help if this is related to simple nausea and gastrointestinal irritation.
I would not feed him any food for 24 hours after the acid reducers are started.
This should help stop gut spasms and restore normal gut motility. Small amounts of water given frequently are fine as he needs fluids after all that he has lost with loose stools and vomiting. You can give him pedialyte to replace electrolytes too but Gatorade is much too high in sugar which can make his intestinal irritation worse.
Today even with the fast you can start Kao-pectate at 1ml per pound or 1 tablespoon per 15 pounds of body weight every 6 to 8 hours. This is quite safe and will coat his irritated gastrointestinal tract as well as absorbing bacterial toxins. You can use it until his stools are firing up, several days if necessary. You can find kao-pectate at the drug store.
If he has a tense painful abdomen, continues to have loose stools after being on
kao pectate for 24 to 48 hours, becomes very lethargic, continues vomiting consistently or runs a fever greater than 103.5F then he really must be seen by a veterinarian as soon as possible. Make sure to take a fresh stool sample with you when you go.
After his food fast start a bland diet of 2/3 boiled white, skinless chicken, all fats and juices drained off mixed with 1/3 boiled, plain white rice. Feed several small meals a day. You might wish to add 1 to 2 tablespoon(s) of canned pumpkin to each meal if you are seeing mucous in his stool as fiber helps soothe an irritated colon.
Once he feels better (no diarrhea or vomiting for 48 hours) start mixing in what will be his regular cat food very slowly. You might want to try a sensitive stomach cat food. Both Hills Science Diet and Royal Canin make these foods. When you start reintroducing a regular diet feed less bland and more regular with each meal. It should take a week or so to convert him back.
If he is continuing to vomit and starts feeling poorly though it would be best that he see his regular veterinarian now as anything you give him orally will just come back up worsening his dehydration.
If this continues to happen to her with clear fecal checks then discuss using a hypoallergenic diet with your veterinarian, such as Royal Canin Duck & Green Pea or further diagnostics to look for an underlying cause for her gastrointestinal upset. I would recommend a complete blood count, biochemistry profile, fel spec PL (for pancreatitis) and probably other tests based upon those results such as an abdominal ultrasound.
Please let me know if you have any further questions.