Why Does My Bathroom Water Sting And Makes Me Itch. What Is In My Water?

If the area where you live supplies fluoridated water, (That is, Fluoride added to the city water at the water plant)
You may have a sensitivity to Fluoride. The amount of Fluoride added to a city's water is not well regulated & Some cities add more than twice as much as other areas. Even if you are not sensitive to the fluoride in your toothpaste, excessive amounts of fluoride can overwhelm the body, and cause an allergic reaction.
Do some research, about the amount of Fluoride your area's water contains.
The reaction you described sounds consistent with hives (large, red, itchy welts that can appear almost anywhere on the body after encountering an allergy trigger they can grow in size and multiply in number the more you itch them, and can last anywhere from twenty minutes to several days). Hives can occur for many different types of allergic reactions, but if you are experiencing hives after showering, I would guess your allergy is to fluoride.

The only time I ever experienced this was after I moved to the mid-west and found out just what "hard" water was about.  There was no water softener in the home we first lived in, and as a result, all the mineral deposits in our water were actually being retained on our skin and scalp when we rinsed after showering.  If this is the case with you, you will find your skin to be very dry, maybe white and flaky.  If you're prone to any skin condition like excema, it will cause breakouts (sometimes looking like a red mark that may have a scaley look).  Good indications that your water needs softening is that your clothes will begin to look dull and have a not-so-soft feel to them after drying, soap will barely lather on a washcloth, you end up using twice as much soap, detergents, shampoo, etc.  Faucets and tanks will have a white, ashy deposit on them. 
You may want to try a good body cream like Neutrogena to ease the itching.  If these suggestions don't work, or don't pertain to your situation, sometimes it's a good idea to make an appointment with a dermatologist, and see if there's a medical problem, like excema or psoriasis, or even an allergy to the type of soap you may be using.
Hope that helped you out a bit!
Moe

have you been using a new type of bubble bath?
Or shampoo/conditioner
because you could be allergic to them!