Friend, he is drooling likely as a consequence of vomiting, he could be nausea. The big question is: Why is he lethargic and vomiting? These symptoms can be caused by many different conditions. It will be difficult for me to determine the exact underlying cause without a hands on examination and some testing. But, common causes are: A simple gastritis, dietary indiscretion, pancreatitis, ingestion of a foreign body, infections, etc. to name a few causes. To determine the exact underlying cause he will need a hands on examination with family veterinarian and xrays as initial screening test. In the meantime, in any case of vomiting the first thing to do is give the stomach time to rest. This is what you can do:
1- Do not give things like Pepto Bismol or imodium. Start him on Pepcid AC (famotidine) 10mg 1/2 tablet every 12 hours for the next 2-3 days. You can buy Pepcid AC over the counter in any pharmacy. This will help settle his stomach.
2- No food or water for 8-12 hours. Need to give his gastrointestinal tract time to rest.
3- After 8-12 hours offer a small amount of water. Wait half hour, if no vomiting, offer small amount of rice (50%) and boiled boneless chicken or ground beef (50%) 4-6 times a day. Keep him on this diet for several days then wean him into his regular diet.
4- Follow up with your family veterinarian for a hands on examination.
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