Get a Zinc only supplement and a vit E only supplement... you need more of them... this is the reason why you are having this skin reaction.
I do not see any problem with using soap. As soon as you have augmented your Zc and E intake you will not have a problem with your skin anymore.
Vaginal yeast infection... however do not depend on how clean you are down there, but rather on how clean your bowels are. So depending on the state of your bowels, you might get or not get other vaginal yeast.