You may have dead skin on your lips from them getting chapped or the cold wheather. If so, try exfoliating your lips to get the skin off. Mary-Kay makes a lip exfoliant or you can just do it at home.
Put a good amount of lip balm on your lips let it sit for a minute then take a toothbrush and go in little circles all over your lips. Do this a few times so you get all the skin off then wipe the balm off with a warm cloth and apply a fesh coating of lip balm/moisturizer to keep them soft!
I always apply a lip balm before putting on lip products and I have never had this problem. My favorite lip balm is Burt's Bees Beeswax Lip Blam. It keeps my lips supersoft and has a pepperminty feel that I love!