Yes,Hydrogen Peroxide is caustic. Do not get it on your skin.
I pour all of my chemicals into a pipe that I added to the exit of my septic tank. See the photos I provided that shows the riser on the exit side of my tank. You will see a 4 inch pipe attached to the exit baffle.
I also have a riser added to the input side of the septic tank, see photo. The risers are ESSENTIAL to do tank maintenance.