H2O2 made part of my fingers bleached?

It’s a mild chemical burn (or a bunch of capillary embolisms if you want to get technical). If it hurts, you can soak it in water for 20 minutes or so. The white color will go away on its own as you heal. To avoid this in the future, use gloves if you can.

Your dead cells will eventually shed, revealing new, unbleached skin below.

A scientist and a cowboy walked into a bar.
“I’ll have an H2O,” the scientist said.
“I’ll have an H2O too,” the cowboy said.
The cowboy died.

What was the concentration of the H2O2?

3% H2O2 shouldn’t burn your skin unless you left your hand soaking in it for a long time.

One time I burned my hand with 30% H2O2 while working in a medical research lab. The skin on my fingers quickly turned white. There was no pain. A medical doctor just told me to wear gloves next time I worked with 30% H2O2. No harm done.