Besides inhaling chlorine and disinfection byproducts sent airborne by your hot shower, you also may be inhaling and absorbing radon, an odorless, radioactive gas. According to the United States Environmental Protection Agency, radon is the second most frequent cause of lung cancer, after cigarette smoking.
Radon is currently found in one third of all water supplies in America. That's right, you have a one in three chance of having this byproduct of decaying uranium going onto your skin and into your lungs every day -- if you are one of the unfortunate people with this poison in your water supply.
I would encourage you to spend the money necessary to test for this poison if you get your water from an underground well. Most municipal water supplies do not contain radon.