I don't have shower problems but I can definitely smell the chlorine when I shower. My mom however does have sensitive skin and used to scratch like crazy because of the water. I bought this a few years ago and she doesn't complain anymore. If you can't get this one, find another with decent reviews. Also you might want to get a water filter for your sink too.
Sprite HO2-WH-M Universal Shower Filter
I'm from the same area - http://www.amazon.com/gp/product/B006LQPJIU?psc=1&redirect=true&ref_=oh_aui_detailpage_o06_s00
Works great.