Well the peeling started off for me about 2 months after i turned 21 and moved to a different state. And it just happened out of the blue. In July this will be about 2 years dealing with this. I agree this problem is extremely psycological, but the thing is you have to come to accept it and deal with it the best way you can. Otherwise it will ruin your life. For the 1st year i was thinking about my lips always and constantly looking in the mirror all the time etc...
The only thing i can do is control the peeling the best i can.. which means wearing lip balm throughout the day. for me this isn't a big deal because b4 i had the peeling i used to always use blistex. Letting my lips get dry and peel isnt a option for me. i have tried it a few times and it definitely doesn't help. What works for me is to put lip balm on my lips before bed this is key because for me my lips basically grow skin or whatever while i am sleeping. So when i wake up i can just reapply lip balm and gently wipe of the dead skin and i am good to go for the day.
Also what is helping me is take l-lysine 1000mg in the morning and another 1000mg right before i goto sleep this has helped me tremendously. I seriously have very little peeling in the morning most of the time there is nothing at all. But my lips still get/feel extremely dry if i don't not apply lip balm... there is something wrong with my lips they aren't functioning properly.
About a cure or treatment, i don't know if there is one because for 1 this problem seems really rare and it isn't life threatening. So it doesn't seem to be a priority.