What's making my inside lips feel fluffy and peel?

I'm trying to find the perfect lip balm to use, it seems I might have sensitive lips?

Some lip balms are making the inside of my lips feel fluffy and peel a little, it doesn't hurt or anything but I don't like the feeling. So far Hurraw Vanilla, Dr Bronners Unscented and Burts Bees all cause the peeling. The only one that doesn't is by a brand called Attitude but I can't stand the paper packaging. Does anyone know what ingredient could be the cause from those names?

Any help greatly appreciated.