What's goin on with my hand? Bleach or Snow?

This has been going on for about 7 days now. First it started out with a raw itching burning feel around my knuckles on my right hand. I think a little bit on my left hand too. It looked noticeably red and if I looked closely I could see very small little red spots like openings in my skin. This was the first night and that day i played outside in the snow until my hands started hurting and "burning" like crazy...but then the next day I did the dishes. When i do the dishes i use bleach, only a little though, and only my right hand is in the dishwater i use to clean with, from about my knuckles down. When i pulled my hands out, my right hand was discolored and pale grey-ish(im black by the way) from my knuckles to my finger-tips. in this area my hands were significantly soggy, my skin a little swollen and saggy, and when i made a fist I could see cracks/openings on my knuckles and joint areas. But the rest of my hand was fine, and my left hand was fine. then it started to burn and make my right hand feel very raw when i ran hot water. I notice some of the same feelings and symptoms on my left hand, thought not as noticeable and only on the right side. Now, the joint area and knuckles on my right hand are super dry and rough and have tiny scabs speckled all over, with areas on the right side of my left hand being the same. So...what caused this?? The snow? Or the water? Could it be the bleach, even though I've been doing this for a while now and never had a problem? Will this problem go away and how can i make it better?