I've been taping my hands forever and it does help - especially for pull-ups. Unfortunately I must be gripping the pull-up bar funny because I tear up my palms and fingers. I think it either has something to do with heat, humidity, or the phase of the moon! Taping does help so learn how to do it well or get me to help you before the WOD.
The other option is to wear gloves (never, ever wear gloves!) or use something like Lynx Performance Grips. These grips are basically curved silicone pads that allow you to do pull-ups all night long without tearing up your hands. I have had several pair in the gym over the last couple weeks and I've let some people use them and I've got amazing feedback. So amazing that I bought a bunch of them for you guys to purchase so that you can be tear free! They are going to be selling for $15.00 a pair - and I would suggest that you mark them with your initials so that you don't lose them.
BTW - you'll thank me for picking these up... and keep your paws off of mine! :)