Hi everyone! I'm new to the forum, and I need help with my barrel cactus cutting :)

So I have some kind of unidentified barrel cactus that has had a rough time lately. I keep it in a pot on my dorm window sill, so it's an indoor plant only.

It was rotting from the base up, so I read on the internet that I could attempt to make a cutting and re-plant it, since it would probably die if the base was dead. So my boyfriend and I chopped it in half *gulp* and then I coated the wound with hydrogen peroxide to keep it clean and encourage it to heal faster. So now the wound has "scabbed over" and I want to try to re-plant it.

So I'm now wondering how I should go about potting the other half of my cactus (it's pretty large, it's about grape fruit sized) and if I've been doing the right thing so far.

Thanks in advance for your advice! :)

P.S. Oh! And I've been keeping the cutting upside down in a container in the sun, and putting water in the container hoping it can "drink" some of the water vapor when it's stoma open. The cactus is not touching the water though. I hope this is helping it?