C.H.
My son was also very sensitive to dairy when I nursed, so I had to cut it out. Now, even as a toddler, he won't drink it. He's not even fond of cheese. My husband was lactose intolerant as a baby, and supposedly grew out of it, but both of them have had tons of ear infections. So I now think they haven't outgrown it, and I'm cutting out dairy (except for a few cheese safe for lactose people) as an experiment. My husband's mom has adult-onset lactose intolerance.
My daughter spit up tons, but never seemed to have any problems with milk. My son had some reflux issues, but never needed medications. One major difference: between kids I was diagnosed with food allergies. I'd eaten all the offending foods with my daughter, but not my son. Both kids appear to have the same food allergies as I do.
It can take 3 days to know if something is irritating to a baby. Some irritations will become apparent sooner, but others take the 3 days.
Drinking more milk helps. There's also a "new mom's tea" (herbal) at Whole Foods that was very effective in helping my supply get going.