I've had KP all my life! And it covers 98% of my body.
I also have very sensitive skin. About 6 months ago I started using natural/organic body products. I made sure that they didn't contain any Sodium Lauryl/Laureth Sulphate, parabens, petroleum by products and any other ingredient which was harmful. Where my bumps use to be white or yellow and puss filled, they're now smooth with only a few red dots here and there. Whilst its not completely gone, I can live with some red spots, the yellow ones are gross. My skin also feels soooo much better! My fore arms have cleared up completely as well as my upper thighs. I use a local product called African Organics and I'm extremely happy with it, not just the body wash, but their lotion as well as my skin is no longer dry! I tried using a normal cream the other day with all the bad stuff in (baby cream) and my arms broke out in a bumpy rash!
Please check what you're using and Google the ingredients, some of them will shock you!