No I didn't just wake up with normal lips. It happened gradually over a period of 5 or so days. I noticed a new layer of skin--identified by the vertical lines--around the third day. There was still swelling and a little burning sensation then. The fourth day, I believe, I exfoliated dead skin off the new skin after I brushed my teeth. By the sixth day, I was totally normal. The swelling had gone, the new skin was intact, and I switched the chapstick instead of the semi-permanent aquaphor covering. And now I'm alright.
As for your problem. I'm not sure what you meant to say...thin layer or thick? Either way, I think that this is probably just dead skin (though I'm not sure what you're referring to...I'm just guessing). Which is NORMAL. Some people build up more than others--you just need to exfoliate with a good lip scrub and a toothbrush every couple of days and keep your lips healthily moisturized. It's like dandruff--everyone gets it, but some have more of a problem with it than others. It's normal. That's why Head & Shoulders sell; that's why lip scrubs sell. If you don't have scabs forming every freakin day or two, if you don't get white gunk on your lips whenever you touch water, then I personally consider you healed. Your only problem is maintenance (if I understand you, that is)--just like nails have to be cut, just like dead skin on those nails need to be cut, just like hair needs to be cut, you need to maintain your lips for aesthetic appearance. If you don't care about how they look then you're totally fine, and I believe you can go through life simply licking them moist.
And if I'm wrong, if what you have is just a white line of dead skin forming every so often (how often by the way, and how hard is it to remove?), then you should rejoice. There are much worse things in this world to deal with. You got through the bad part. (But I'd appreciate more detail about what you're dealing with. It might be worse than I think).