The only similar word I can think of is the word "horny." I can't think of another single word that is dedicated to craving something. However, the word "fiend" also comes to mind, as in "people who crave drugs are dope fiends." Google defines fiends as "an evil spirit or demon" which makes sense. To me, it is that intense and deep craving or desire to acquire something and get the satisfaction you want from it. It's also commonly used as "I'm fiending..." for crack or for sex or for alcohol or whatever you need at the particular moment in time. That is the only thing on your mind and you are unable to think or function at 100% until you get it. I've heard it used in pretty ridiculous situations, like "after he took that bong rip he was fiending for some doritos." I don't know how universal this word is though. It's common in my circles of friends - even the ones who aren't druggies. It's just a word that works for a lot of things and lets your cravings and desires be known. As it has been used more and more, the ugly connotations and image of a drug fueled heroin head wondering the street is no longer attached to it. The power of the word remains though. I like the word. It gets it's meaning across instantly. But I find the concept of "fiending for milk" is a bit odd because milk is commonly associated with newborns and children and therefore has ties to innocence. To put milk + fiend in such proximity is a bit jarring but it does get your point across. A quick google search reveals that it has been used before. There is a blog dedicated to cooking without dairy: Dairy Free Dairy Fiend. There is also a dark but pretty cute video of a cat who is obsessively attempting to get the milk from her master's bowl as her master is still eating. And another more properly lit video. And a baby. D'awwww. Although you could just say "I'm craving milk." It takes about the amount of time to say.There should be a specific word for being milk-thirsty.
Funny- I always just kind of saw horny as another delineation of hunger. The way you just put it almost flipped it around so that hunger is more a delineation of being horny. Next time I want to eat, I'm going to tell everybody that I'm food-horny, and see where it gets me. Maybe jail, depending on whether I'm at home or in a restaurant.