E.,
To me, this really screams food allergy. My 5 month old son is intolerant to dairy, soy, eggs, caffeine and chocolate. Before I eliminated dairy and soy from my diet, he constantly had a skin rash. Most babies who are sensitive to dairy are also sensitive to soy because the proteins are really similar. Rather than a pediatric skin allergist, I'd see a pediatric GI doctor first. Of course, if you've changed anything lately like your body wash, lotion, laundry detergent, you want to keep that in mind. If you've recently had your carpets cleaned, you may want to clean them again with just water (there is usually lots of soap residue left in the carpet that is why they get so dirty looking so fast after you have them cleaned). I wouldn't be worried too much about lead unless your place is older than 1978. Since my son has such bad food intolerances (and intolerances are different from allergies but can cause a lot of the same symptoms), we have to introduce foods one at a time for 2 weeks instead of 3 days....
Mold can be a huge health problem so if you think you have mold, I'd call the city offices to see if you can get an inspection. If your place was built before 1978, you can ask them about testing for lead also. If you use a lot of air fresheners, candles and that type of thing, quit. Most of them are full of petroleum chemicals and many candles contain lead. There is no regulation of air fresheners and candles but they can seriously increase the toxic load in your house, along with many cleaning chemicals. You may want to consider using lemon juice, vinegar and baking soda (I'm a big fan on Mr Clean Magic Erasers and try to avoid most chemical cleansers because they burn my skin) for all but your dirtiest messes until you figure out what is bugging you and your son so badly.
I'd definitely quit using dreft. It has a lot of perfume in it. Switch the a "free and clear" detergent. All makes a good one that isn't too expensive. I have sensitive skin too but even mine has improved dramatically since I eliminated dairy, soy and eggs (I'm a breastfeeder too!)
The "big" food allergy suspects are dairy, soy, eggs, chocolate, caffeine, nuts, citrus and tomatoes.
Hopefully you can find some relief soon. It is really miserable when you are miserable and you don't even know where to start to find relief.
T.