Hi my lips only went yellow in the period of my early teens and when i was a meat eater plus excessive junk! After I stopped eating red meat and chicken and stopped using lip salves and switched to almond or olive oil, there was no white mush, just a dry white papery skin that would turn white when drinking coffee or in the shower etc.
Your lips are peeling at different times, you can brush them lightly only to encourage what already wants to come off, then continue the soak and you will see it will peel off itself.
Each cycle of peeling will get less and less until it should stop altogether, assuming your condition is fungal. I wouldnt bother about why the lips at sides peeling different to other part of your lips by the time you have done the protocol hopefully all of your lips should stop peeling anyway.