Do you mean just direct dairy foods (eggs, milk) or anything with milk, eggs, cheese, etc, in it (pizza, cake)?
Well, speaking for me...
I started with milk - and that made a dramatic improvement. Cheese was another big one for me - I try to avoid pizza because when I eat it my sinuses swell up and I can even get a headache.
I don't go out of my way to avoid stuff made with milk byproduct (and of course once a month I may have to eat a buttered bagel or pizza slice when out with friends - however I religiously avoid straight-up cow milk and very seldomly eat straight-up cheese). Incidentally - I also try to avoid refined sugar as much as possible, so I don't regularly eat deserts beyond simple stuff like fruit.
It took about a week for me to start seeing the improvement (I think it the allergy stayed in my body for a while)
Eggs don't cause me a problem (I'm not sure if they are dairy)
I wasn't as bad off as you - for me it was that I stopped having my sinuses clog up at night, frequent sinus infections, stomach issues, splitting sinus headaches, ringing ears, really my whole life is better. No doc ever told this to me (out of two docs, a nurse practitioner, and an ENT doc - one thought it was simply a temp change thing - I do have sensitive sinuses to temp/pollution, but it seems when dairy is added that's the magic formula for trouble). I read up on cow milk and some ppl just can't handle it's overabundance in the typical American diet.
I figure it's worth a shot for ya - I hope this helps...