What Causes Burning Sensation And Spot Below The Knuckle After Using Bleach?

I was cleaning my bathtub with no gloves on, using products that contained bleach. I don't know what happened, but I looked down at my thumb a little later, and there was a small spot below the knuckle with blood. I thought I had cut myself. I wiped it away, but I saw no cut. It's not bleeding or anything, but now the area is red, swollen, and a bit tender. I feel a burning sensation coming from the area. At this point, the area is a bit smaller than the size of a dime, surrounded by red and a little whiter in the middle and swollen. Any ideas?