Sorry your having such issues with your baby.
My Murphy had bloody diarraha when I got him and he used to vomit and didnt seem to get better. The Vet had to run serveral Stool samples to confrim Coccidia. He was put on Meds for his tummy and Meds for the Coccidia. He was eating at that time, Royal Canine Dry Puppy food, but didnt seem to be good with it. His tummy made Noises like it was churning or grinding. The Vet had him on I/D for awhile and then we switched to one ingredient soft food like Rabbit. He ate this for awhile till his tummy calmed down and when he was well enough we switched it over to Wellness Just for Puppy Dry, and he loves it. No more running poop, No more Tummy Grinding, he runs and plays and is such alittle terror he is 8 months old 4 lbs
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Please have your vet do stool samples to look for these problems if they havnt done it yet. Good luck, keep me posted.