I always have dry chapped lips... it's probably genetic or something because my mom has them too, she has a lot of dermatological problems, and I'm glad that *so far* I don't think I've inherited them all. Mine have never been as bad as what you have described, but I use burts beeswax lip balm and it seems to work better for me than blistex medicated. But you may have to re-apply frequently.
Good luck

I know that when chapped lips get *really* bad they can get really painful.