Hi J.---Your daughter is trying to tell you something. Cows milk is not good for her...or anyone else's...body. Cows milk is designed very specifically for a baby cow to grow into a huge animal very quickly. A mammal's milk is designed specifically for that species.
I am a reformed cows milk drinker. Several years ago I started taking classes, taught by a Naturopath who has her PhD in Nutrition. I've learned some very interesting things, many of which run counter to commonly accepted 'medical' advice. One of them is the dairy issue.
But don't take my word for it. Please go to www.pcrm.org and put dairy in the search box. Some additional info can be found at www.notmilk.com and at www.thechinastudy.com. Keep in mind, our dietary advice/food pyramid comes from the USDA, a gov't entity set up to PROMOTE US agriculture. They are NOT a health organization. As such, they are very heavily influenced by industry trade groups. Just something to keep in mind as you make decisions that are best for your family. Plant milks are a great option for your daughter, although it is best for her to just drink water and use the milks 'in' things, like her cereal, smoothies, etc. BTW, I have a great smoothie recipe that is super healthy and super yummy.
It is true, as another posted stated, that there are really very few true food allergies. Most are food sensitivities and the answer for that is a balanced diet that will help the body heal itself. But there lies the problem. How do we get her to eat a wide variety of foods without them causing her distress? I think I can help.
I have some great ideas that I can share with you, that I've learned from the Naturopath and from docs like Bill and Jim Sears (ABC's The Doctors, www.askDrSears.com). Please feel free to contact me and pick my brain. Let's see if we can get your little one moving in a forward and positive direction. Good luck with your search to help your baby. D.