E.B.
My daughter has had to undergo several food elimination trials (one food at a time).
First, you should know that one week is generally considered insufficient for a food elimination. Many elimination trials consist of a 3 or 4 week (or more) period of time.
Second, just to be clear - it's more than milk, cheese and butter. Look up all the words that indicate dairy (whey, casein, etc) on a reputable website (Mayo Clinic etc) and be sure that you are eliminating all those sources. That's the only way you'll be assured of a dairy-free trial.
Third, keep a journal, a food log. And be specific. If your daughter is out with friends and can't (or won't) write down PRECISELY what she's eating, have her take a photo with her phone of either the foods or the item on the menu that she ordered. Later, you both can enter the foods into the journal. You may notice other culprits on the food journal. If she's eating only snack food and processed foods and "junk" food, and drinking diet sodas, the answer may be as simple as swapping in some fresh vegetables and fresh fruits and eliminating the diet/sugar-free stuff.
My daughter does not have an intolerance to dairy or most of the foods that we tried eliminating, but she does have a severe and debilitating and documented intolerance to the artificial sweeteners (all the xylitols, mannitols, sorbitols, sucralose, aspartame, etc). They give her extreme stomach pain and intestinal cramps. If your daughter is chewing sugar free gum and downing sugar free sodas, and eating "diet" foods (low-fat sour cream, fat-free cheeses, etc, which often can contain artificial sugars), that might be where the problem lies. And it can be tricky. For example, I recently saw a coffee creamer that said "sugar free" on the label (I don't use it, but I happened to notice it). But in the ingredients list was "sucralose" which is Splenda. So you might have your daughter examine her sugar free habits, and have her drink water, orange juice or sparkling (non-flavored, non-sweetened) water, with maybe some fruit in it. And skip the sugar free gum/mints/candies. They can really be painful for many people.
Hope that helps!