When I got my puppy he also had similar problems for some time, upset tummy and vomiting but I fed him kitchen food gradually along with vet recommended(Found a specialized vet online, you can check greatvet.com or vetstreet.com for assistance). I think for your case you might wanna consider kibble brand (your vet recommended) as it’s the matter of your pet’s health. Also, try to figure out your dog’s allergies - mine is allergic to fish - which I figured much later, after a month of indigestion.
Our pup (11 weeks) had a dodgy tummy for the first ten days we had him. He came on Skinners Trial and Field but we have now switched him to Orijen Large puppy which has firmed things up nicely The vet also gave him a probiotic for a few days.
