milkaholic
n. A person addicted to milk.
Etymology
Examples
1997
A 61-year-old man in Seattle who loves milk, and describes himself as a milkaholic, had a minor stroke a few years ago, and he has now filed a federal lawsuit against the supermarket chain where he bought most of his milk over the years and the Dairy Farmers Association of Washington for their failure to put warning labels on the milk cartons.
—Charles Osgood, “Man sues dairy farmers and grocery store for offering milk without warning labels,” CBS News Transcripts, June 06, 1997
1987
Norton is an admitted "milkaholic." "That’s the one thing I’m addicted to. I can’t get enough. I drink more than 10 glasses a day."
—Jeannine Stein, “Teen-age trilogy,” Los Angeles Times, October 04, 1987
1965 (earliest)
Although there may be other causes for a big "healthy-looking baby staying sickly," we can find the answer to your baby's problem in your letter. Your baby is a "milkaholic."
—William G. Crook, “Excessive milk intake causes iron deficiency,” The Kokomo Morning Times, May 12, 1965