R.B.
I didn't think you are supposed to give a baby under one year cow's milk - and I thought it was because it's harder on their system / doesn't provide enough of the important ingredients for adequate growth, etc. for a baby that young. I don't know for sure the reasoning behind waiting until after a year, but that could be why when given too much, your 11 month old can't handle it.
Also, if there is a true milk allergy, there would be blood in the stool (sometimes too small to detect with the naked eye - so they'd have to test it in the lab). Maybe your doctor could order that test to be sure. Does your baby cry after eating (as if belly pains)?