Yes! My dd had blood in her stool at from about 4 weeks of age, we went to see 2 peds and a hospital visit to find out the problem. It was only a random doctor at the hospital that was chatting with us and happened to ask why we were there that said "oh, blood? your dd has a milk PROTEIN allergy (different from a lactose intolerance)". I had to eliminate all milk products/byproducts from my diet until she was 18 months. The odd time someone would screw up in a restaurant and I had a milk product in my meal (without taste or knowing it) she would end up with blood in her stool the next day. BTW, don't know why so many doctors are ignorant to this, it's not "rare", aside from the other moms on here dealing with milk protein allergies, 3 of my good friends los have/had los with it too that have actually had blood in their stools from milk products right up until they got over their allergies.
My lo was able to tolerate plain yogurt around 14 months, but not cow's milk until about 18 months. At 12 months we started fortified unsweetened rice milk and I continued to bf until 18 months. You can always try the formula that is hypo non-allergenic. The only thing we had to watch with the rice milk and no milk products was keeping up her fat intake as she missed so many calories from milk products. Our ped gave us a list of foods for her to eat that were higher in cals and fat than others. Also recommended stuff like chicken legs with skin and fat on vs. white chicken breast with no skin, etc. Basically most of her fats were from protein foods.
I'd wait until the blood clears, then try again but with plain yogurt. I'd do the butter and milk last. Our allergist did say to start challenging at 12 months and try every few weeks or month.