My childhood was exactly the same. Something else happened that would hint at something like this though, which was lots of weight loss (and I was quite overweight). I am actually suspecting I've got lyme disease, but I know I have had candida to a degree.
Instead of having eczema like you, I have gotten a face full of acne, which I have managed to keep calm through colon cleansing and eating enough fiber.
I'm really interested in what probiotics do us the best, but of course we are all different. Keep us updated!