I would recommend hitting the organic foods section at your supermarket (or a health food market) as they will have far more options. In general, you do have to make more stuff yourself, but the ingredient list tends to be much shorter on the organic stuff - granted, it's pricey in some cases, but assuming you're not gluten free too, finding a nice dairy-free pancake mix for a quick lunch with the kiddos is so helpful. The other good thing about going to these stores (especially smaller, boutique ones) is that the staff have loads of good advice and can point you at some products you might never otherwise have tried.
As for sensitivity, I can scarce believe how little can set my DS2 off - a few weeks ago, I had a bite of steak (which I had ordered along with an undressed salad at a restaurant), I immediately told DH that there was butter on my steak. He thought I was being ridiculous but when you haven't eaten it for awhile (and I like it!) it stuck out like a sore thumb. We checked with the waitress and sure enough, it had been brushed with garlic butter. The little guy was off for 3 days off just that one bite!
For milk replacements, I'd suggest giving a few different brands of whatever you choose a try... I've found a big variance in texture, flavor, etc from one to another.