That was very long and a lot of details!
I feel like you are too much concerned about many small details, but you are missing the bigger picture.
It doesn't really matter much what consistency is the dead skin on your lips, after the shower. It is dead. It died just like top layer on your other parts of your body die from what is called eczema.
How long time have you had eczema?
Do you know what triggers your eczema ?