can't help you with the shampoo, but...
how is your water quality? if it's very hard that may be drying out your skin. the pool chlorine will do that too. so can a house that is too dry and over-heated. you may also be dehydrated or under-consuming fats. a soap that leaves an oily film on my skin just sounds gross, and like something that would a) rub off when i got dressed and b) stain my clothing. i'd really focus on getting hydrated from the inside.
i don't wash with soap unless a washcloth can't scrub off the dirt. then i use dr. bonners castile soap.
As I ate the oysters with their strong taste of the sea and their faint metallic taste that the cold white wine washed away, leaving only the sea taste and the succulent texture, and as I drank their cold liquid from each shell and washed it down with the crisp taste of the wine, I lost the empty feeling and began to be happy and to make plans.
– Ernest Hemingway