warthog
I did go through a period where my lips peeled. Then it went away. Then it returned briefly. I considered it part of some kind of cleansing-healing process. I never bothered to change oils because of it...I use Hain sunflower oil all the time.
In general, now, my lips are soft and smooth. Even though I live in a desert, I found that I rarely need a lip balm, while previously, I would apply something in the evening before bed & in the morning after breakfast.