Your story sounds exactly like mine, except I was able to figure out somewhat early on in my oldest child's infancy that the cow's dairy products I was taking in were coming through MY milk. My oldest child was MISERABLE until my system cleared itself of the dairy intake - takes up to 2 whole weeks. And then - WHAM - she started sleeping through the night - thank goodness because I was totally sleep-deprived until then due to her crankiness and colickyness and crying/screaming fits.
I hadn't planned to use formula at all and had NO idea that it was based upon cow's milk. My son was so fussy that I couldn't stand to try to nurse him because he would wiggle and cry and fuss. I gave him a bottle and within a couple of minutes I noticed that the bottle was leaking.
I took the bottle away and began taking off his clothes to clean him up and he was nothing but red welts where the formula had come into contact with his skin. He'd only had the bottle a few minutes! I cringe to think what it must have been doing to his tummy!