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.