I'm not sure how to best describe this, but sometimes after I climb, I feel lots of pain the tips of my fingers and tips of my fingernails. It feels like my finger nails are being pulled off--sort of like when you cut the nail way too short. It lasts for a couple days, and sometimes warm water seems to really aggravate it.

Does anyone know what this is called or how to treat/avoid it?

I get the same thing sometimes. Putting moisturizer on your finger tips can help. Try to cut your fingernails before you take a few rest days rather than before you climb. Wearing gloves for a while helps too. Other than that, no pain, no gain...

I get the same feeling if I climb with nails that are too long, too, short (like right after cutting them to the quick), or just too many fingernail crimps.