I have a 2yo daughter with severe eczema triggered by food allergies, and I definitely think that vaccinations are a part of the puzzle. My dd was vaccinated up to 1 year. By vaccinating, we bypass our body's first line of defense- the skin and mucus membanes. Our body works hard to keep the blood stream sterile, and easily fights off most bacterias at the skin level- only a virulent bacteria or living virus is able to get through the first line of defense- but when we vaccinate, we take harmless killed or weakened bacteria or viruses (and lots of other junk) and place it right in the blood stream, and we do this in very young infants, forcing the body to create an immune response to harmless microbes. I personally believe, though I can't back myself up with medical studies or anythink like that, that vaccinating can make the immune system overly sensitized- so it attacks things that aren't a threat, like in my daughter's case, protiens from peanuts, eggs and a numbe of other things.
I don't know about the yeast over growth. You may want to consider that dairy and meat, unless organically grown, are also laced with antibiotics.