Based on the signs you have reported, I'd be concerned that your son's dog has a GI infection brewing causing both nausea (which is what would put him off food/water) and the diarrhea. We can see these signs with dietary indiscretions, pancreatitis, and ingestion of foreign bodies as well; but hose usually won't make them feel febrile as you have noted here. Though I do have to note that if that belly looks distended or you notice any pain in that region, then we'd also have to be concerned of possible bloat or gut twists (less likely with fever, but something we do need to keep an eye out for since they are urgent when they arise).
With this all in mind, we can try some home supportive care to try to settle his stomach. To start, if he hasn’t just vomited (since otherwise we’d need to rest his stomach for a few hours first), then you can consider treating him with an antacid. Common OTC pet safe options would be Pepcid (More Info/Dose @http://www.petplace.com/article/drug-library/library/over-the-counter/famotidine-pepcid) or Zantac (More Info/Dose @ http://www.petplace.com/article/drug-library/library/over-the-counter/ranitidine-hcl-zantac). Whichever you choose, we’d give this 20 minutes before offering food to allow absorption. Of course, do double check with your vet if he has a known health issues or is on any medications you haven't mentioned. And if he isn't able to keep these down, then that would be a red flag that we need your local vet to bypass his mouth with injectable treatment.
Though if he keeps that down and he is steadier on his stomach, you can consider starting him on a light/easily digestible diet. Examples you can use are cooked white rice with boiled chicken, boiled white fish, cottage cheese, or scrambled eggs (made with water and not milk). The aim of these diets is that they will be better tolerated/absorbed by the compromised gut. Therefore, it should get more nutrients in and result in less GI upset and diarrhea.
Finally, if his stools are very runny, you can also consider trying a pet safe anti-diarrheal. As I am sure you appreciate, these would not be a cure for infectious issues; but it can still be of benefit. It will reduce diarrhea load, allow the body to absorb more water/nutrients, and soothe the upset gut. In regards ***** ***** options, the one we most commonly use is Kaolin/Kaopectate (More Info/Dose @ http://www.petplace.com/article/drug-library/library/over-the-counter/kaolin-and-pectin-kapectolin-k-p)). This is available OTC at most pharmacies. Otherwise, Propectalin, Canikur, Fast Balance, and Protexin Pro-Fiber (which is available OTC at vets, pet stores, and even Amazon) would be another option. All will slow diarrhea and those last ones have the added bonus of providing support to the delicate good GI bacteria. So, these can be used as a short-term means of soothing his upset GI.
Overall, a wide range of agents could trigger these upper and lower GI upset we are seeing. Therefore, in his case, we’d want to start supportive care to settle his stomach. If he cannot keep that or water down, appears dehydrated already, or doesn’t respond to the above within 12-24 hours; then we'd want to get his vet involved. They can assess his hydration, rule out fever, make sure there is nothing in his stomach that shouldn't be there or any sinister viruses present. Depending on their findings, his vet can treat him with injectable anti-vomiting medication, appetite stimulants, fluids, +/- antibiotics to settle his stomach, and get him back feeling like himself.
Please take care,
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