You can get rid of eczema. Its usually a sign of gut disturbance. I have read many cases on the Yeast Connection Forum of people getting rid of it.
The idea is to starve the fungus (yeast) so you have to avoid anything starchy especially sugar, kill the fungus with antifungals, and then replenish with probiotics. So you are on the right track already. But if you don't starve them, they will not completely go away. They survive on starchy foods.
There is another Candida thread you might be interested in . Also, more info is available at www.wholeapproach.com.
http://www.websitetoolbox.com/tool/mb/kiddredd (yeast connection)
About the heavy metals, symptoms can be vary. Some have add type symptoms, food sensitivies including gluten (mercury damages the enzymes necessary for gluten digestion), wierd pains, reoccuring yeast problems, other auto-immune problems, brain fog, autism....the list goes on and on. It can be different for everyone.
If you have yeast problems that keep coming back after many attempts to control it, then you definately have some underlying issues - most commonly heavy metals. Do you have fillings?