Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear about Boo's vomiting and diarrhea.
If he goes outdoors it's possible that he ate something he should not have or was exposed to a parasite, virus, or toxin which could cause his symptoms.
Even if he is an indoor fellow they can sometimes find things to eat that they should not.
If he's had an abrupt change in diet or now treats those are possible reasons too.
If he were an older cat internal organ disease (kidney or liver disease, diabetes), hyperthyroidism, inflammatory bowel disease or cancer could be possible, but are less likely in a 2 year old cat.
Can you take his temperature? Normal temperature is 102F, a fever is greater than 103.5F.
Will he let you feel his belly? It should be soft and he shouldn't be distressed by your palpation. If it is tense or he vomits in response to your palpation that's not normal.
What do his mucous membranes look like? Are they bubblegum pink and smooth feeling? Or do they feel sticky?
If he doesn't have a fever, his belly isn't abnormal and his gums are normal we can try home therapy.
I would not feed him today but if you can get get him to stop vomiting push fluids, make sure he's drinking well, offer pedialyte or syringe it in to keep him hydrated and replace electrolytes.
To settle his stomach you can give him Pepcid-ac (famotidine) at 0.25mg to 0.5mg per pound orally every 12 hours to help settle his stomach. That's 1/4 of a 10mg tablet per 5 to 10 pound cat every 12 hours or 1/2 of a 10mg tablet per 10 to 20 pound cat every 12 hours.
Today even with the fast an hour or so after the Pepcid 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 for several days until his stools look normal. You can find kao-pectate at the drug store. I like the kao-pectate formulation with kaolin and pectin better then Pepto Bismol as Pepto has salicylates which are poorly tolerated by cats.
After no vomiting for 12 hours you can try offering him a bland diet of 2/3 boiled chicken and 1/3 boiled plain white rice. Feed him several small meals rather than one or two large ones. You can feed this for several days until the diarrhea clears. After no diarrhea for a couple days start to mix in his regular food, gradually giving more of his regular diet and less of the bland at each meal each day so over a week's time he's converted back.
If he continues to vomit or starts after introducing solid food again, gets a painful belly or a fever it's time to see his veterinarian.
Keep him indoors until he's normal, at least a week.
I do recommend that you submit a stool sample even if he's improving as this can be parasite related.
Please reply with any further questions.