When I was a child the palm of my hand was red raw and sore. The skin would flake off and it was itchy. The ball of my foot also did it. Cause?

Possible allergy. It could have been an allergic reaction to something coming in contact with both your hands and feet. It could have been a type of eczema called dyshidrosis. It's unlikely that it was athlete's foot, which doesn't typically affect the palms, especially in children. Without seeing the rash, that's about as far as i can take it.