Hello & welcome, I am Dr. B, a licensed veterinarian and I would like to help you today.
Poor Boe! Signs like this make us wary of an infectious gastroenteritis (ie hemorrhagic gastroenteritis, Salmonella, Campylobacter, parvo, etc), or parasite infections (coccidia, Giardia, etc). Now if he is passing a lot of blood or cannot keep even water down, he is best seen urgently. (Vets in our country have to provide out of hours care, so if they do not have Sat. morning surgery you can still ring to reach their out of hours support).
Any delay on that and we can try some steps at home. To counter nausea/vomiting, consider trying an OTC pet safe antacid [ie Pepcid (0.25-0.5 mg per pound every 12-24 hours),Omeprazole (0.25 to 0.5 mg per pound every 24 hours), Esomeprazole (0.25-0.75 mg per pound once daily)].. Of course, do double check with your vet if he has a known health issues or is on any medications you haven't mentioned. Though if he cannot keep it down, that is a red flag that we need to bypass his mouth with injectable anti-vomiting medication from a local/ER vet.
After we can try him with a light/easily digestible diet (Eg rice with boiled chicken, boiled white fish, scrambled eggs, cottage cheese, meat baby food as long as its free of garlic/onion). There are also veterinary diets that can be used(ie Hill’s I/D or Royal Canin’s sensitivity). The easily digestible diet will be better tolerated and absorbed by the compromised gut and should get some nutrients in. Fiber (ie canned pumpkin) and OTC probiotics (ie Benebac, Fortiflora) can be added to these meals to firm those loose stools quicker and support digestion. And those are quite useful since we cannot use anti-diarrheals with those hemorrhagic concerns (as those viral and bacterial agents cannot be allowed to linger in the gut as they can damage it further).
Overall, I do share your concern about your lad. As long as those gums are pink and that belly is comfortable; we can use the above until your vet sees him. Once they are, it would be best for him to have a check with them. If possible, do bring a fresh stool sample so they can see what is passing +/- test it if need be. Depending on their findings, we'd want them to start fluids, antibiotics +/- gastroprotectants if needed to settle this and get him feeling better.