It seems very unlikely to be Celiac. Too much inconsistency. In that case, it may well be an allergy or an array of allergies. Note that white flour is commonly bleached, and that introduces bleaches and byproducts, including sulfites, that are not present in whole wheat flour and its products. The specific allergens can be fiendishly difficult to pin down, but that would be true allergies and not a disease process.
Here's why it's hard to pin down. Let's say it's sulfites. No sulfites in cow's milk, right? Nope. Skim milk is often "filled," and sulfites appear with the oil used as filler. And eggs contain some sulfites. Not too much, but in combination with other sources, it can contribute. Beet sugar gains sulfites in bleaching. Too many foods have added sulfites to list here.
Now, this is not to say it's a sulfite allergy. There are many foods with sulfites, including wine. But it just demonstrates that the villain(s) can lurk in unsuspected places. But when white flour hurts and whole wheat is okay, it's suspect. It can take many trials to even hope to pin down the allergens. If I had a desire for baking with all-purpose flour, I'd test with King Arthur Organic Unbleached All-Purpose Flour. And, in a separate experiment, if I'd found problems with milk when I was using altered milk, I'd try whole milk, a good brand that's unlikely to be filled.
And while fish has caused no problem, if it turns out salmon has bad effects, suspect sulfites. And note that some shellfish is treated with sulfites to fight mold. So, the problem is to restrict to absolutely tried and tested safe foods when testing one and only one suspect food and making that one organic, if possible. Organic is always preferable in this effort. Not because non-organic is automatically bad, but because it eliminates some of the possible allergens. I seems to be harping on sulfites, and it is a known allergen, but it's not necessarily more suspect than anything else.
