If you're replacing the milk with Oreos, that could well be part of the culprit; I have intestinal issues for a couple DAYS after I get hold of those! (I have a friend with a dairy-allergic DD so when they visit we have them in the house...
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I would recommend trying HARD HARD HARD to replace the sugary stuff with veggies, raw if possible, use dressing if it helps, and going cold turkey for mayeb 2-3 days. Also, adding a probiotic to your diet is REALLY helpful; if you're completely dairy-free, though, check to make sure the probiotics aren't dairy-derived, since the easiest way to cultivate them is in..... YOGURT! There are some dairy-free ones, though; look for Culturelle, which makes some that isn't dairy origin. Also, if you're able to tolerate it, raw sauerkraut and kimchee (and other cultured veggies) are good sources of probiotics in non-dairy sources; I can get it near me at Whole Foods, and the kimchee they carry there is particularly yummy! Spicy, but YUMMY!
As an aside, I find that while our family has a hard time with most dairy, unable to digest it (so for us it's an intolerance but not an allergy), yogurt is the one dairy food we can all eat with no ill effects. Apparently the culturing not only pre-digests some of the lactose, but the casein as well.