First, I would just note that his stomach is much lower down then when you are putting pressure. So, he could just be sensitive in general because his stomach hurts or we may have discomfort from an unrelated issue. So, we do need to keep an eye on that.
Now based on the signs we are seeing, we do have a few concerns. Common causes we need to consider include bacterial or viral colitis, whipworms, protozoa (ie coccidia, giardia, etc), general dietary indiscretions, and ingestion of harmful items (thankfully less likely for Max). We can also see blood alongside anal gland issues and those can be quite sore, but usually they are tender around their back end or when the tail is lifted.
So, we do want to tread with care but we can try to soothe his stomach and settle his diarrhea. To start, 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). There are also OTC vet diets that can be used (ie Hill’s I/D or Royal Canin’s sensitivity) too. 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 reduce diarrhea. As well, you can also add fiber (ie canned pumpkin, all bran) to these to just bulk his stool up quicker. As long as improvement is being seen, I usually advise continuing this until the signs are settled, and then weaning him slowly back to his normal diet.
Otherwise, if his stools are very runny and since it was only a few drops, you can 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 the diarrhea we are seeing. Still, the discomfort doesn't fit with this, so we do need to keep an eye on that. Therefore, in his case, we’d want to start supportive care to settle his stomach. If he appears dehydrated already, is very sore, 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, test a stool sample, make sure there is nothing in his stomach that shouldn't be there or any sinister viruses present. They can also check this likely unrelated discomfort (which may just be arthritis at his age). Depending on their findings, his vet can treat him with antibiotics, gut safe pain relief, +/- anti-parasitic treatment to settle his stomach, and get him back feeling like himself.
Please take care,
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