To answer your question, no, my doctor told to leave my lips alone not put any kind of moisturizer (and no peeling of course) because I explained to him that moisturizer make my skin get all mushy and white (like one of the pictures I uploaded in my first post)
It´s a shame that the biologic injections didn´t work for you, but after a quick google search I can see that Dupixent is only used to treat Eczema and not Psoriasis. I could be wrong about and, if am I, please pardon my ignorance. I don´t much yet about these biologic treatments.
I´m going to try to update here every two weeks (every time I get a injection).