Skin rash that involves red, itchy, raised areas of skin, or red lesions with a red "flare" at the borders, are characteristic for condition, known as urticaria or hives.
Skin lesions that are itchy, are easily spread by scratching.
There are different types of urticaria, and you seems to have physical type of urticaria, either aquagenic (reaction to water) or cholinergic (reaction to body heat, like after a hot shower) urticaria.