My fingers get dry and itchy after wearing latex & or plastic gloves, what could be causing this?

An allergic reaction. You might be developing an allergic reaction to either latex or one of the chemicals used to make the gloves. I would recommend avoiding contact with the type of gloves that are bothering you and seeing a board certified allergist or dermatologist to determine what you are allergic to.
Varies. Multiple potential causes, but a latex sensitivity would be a consideration. You could potentially see an allergist and be tested for it.