I have had the peeling lips for the past 15 years. I was always conscientious about it and I never kissed a girl until I was 24 years old. I had some insecurities thinking no girl would ever want to kiss me, but I was totally wrong.
For all you guys or girls out there that are super nervous about kissing someone, don't be. I just peel my lips and put some chapstick on them 24/7 and even though they don't look exactly "normal" its totally fine for kissing. I am starting to kiss different girls and one is telling me she can't get enough of my lips. I told her about my peeling lips but she doesn't care, she LOVES kissing my lips. So don't worry about it too much people. Just peel away the dead skin and live your lives like normal. It isn't going to be a problem as long as you are making your lips somewhat moist. Anyways, this was ALWAYS a insecurity of mine until I found out nobody cares. Just be glad you even HAVE lips because girls tell me they hate kissing guys with no lips at all. As long as you are confident and start kissing all over your partners body and smooching their lips they will not ever notice.
And really, isn't that the main concern for every person that has peeling lips? Whether a person of the opposite sex will accept their lips? Don't worry about it anymore, I promise it isn't an issue, and now I don't even care if I have it forever.