I haven't read the other replies, so apologies in advance if I'm just repeating what's already been said.
there are several ways you could go about this. Now, if you really really want to be positive that this condition isn't a result of what you're eating, you could do a spa fast, and do the enema thing. I'm serious. If you want to know more about it, feel free to PM me. It lasts for seven days, and at the end of it you'll know if it's a food allergy or not.
the thing about soap is, the suds and all that? that is simply a chemical added to soap or shampoo to produce bubbles and suds. it actually does nothing toward cleaning anything. It is there to make you think that the soap or shampoo is cleaning like crazy. All that is necessary for a soap to clean anything is that it contain a surfactant. If I remember right, the surfactant clings to the dirt particles, then, because oil (the surfactant) and water do not mix, water washes both dirt particles and surfactant away.
So, this leads to my next recommendation. Research essential oils and various plants, natural ingredients, to use instead of the usual commercial soaps and things. there is also another chemical put in virtually every soap and shampoo on the market - parabens. I have read that these things can cause skin conditions.
I used to use a mix of rosemary oil, sweet almond oil, cypress, and tea tree oil on my face, but this is an expensive way to go. Now i just use a mix that someone posted here on the forum a while back - castor oil and olive oil to clean my face at night. It works very well. I rub this mix in, steam my face with a washcloth soaked in hot water, then repeat once. After that, I gently rub vaseline on my face and wipe off any excess with cotton squares.
It could be that your skin needs some sort of topical treatment like this, because dry skin can break out too, due to the dryness.
You'll need to experiment with various things. you might check for books on things like natural remedies or concoctions at your local library. hope this helps and good luck!