From my research on the internet (including this forum but also well beyond it), it seems that anti-fungal creams plus hydrocortisone creams plus vaseline are the most common approach that doctors take to cheilitis.

It is my understanding that all of the "-azole" treatments are anti-fungals. Clotrimazole, Miconazole, Ketoconazole, and so on. It seems to be very normal and expected for a doctor to prescribe one of those treatments (or similar) for exfoliating cheilitis.

I would be surprised that your doctors in the past had not already tried giving you a topical anti-fungal.

Unfortunately, I have never seen anyone's testimony that an anti-fungal cream has worked to cure exfoliative cheilitis, and I have asked that question here on this forum several times, with no responses.

It is my hypothesis, though, that the people for whom anti-fungal creams do work to clear their condition are the people who don't spend a lot of time on the internet afterwards talking about their formerly scaly, gruesome lips - they just reasonably forget the whole topic. It is the people for whom no typical treatment works who are the ones that populate discussion forums about cheilitis.

I have tried several types of anti-fungal medications myself, and hydrocortisone with and without anti-fungals, and vaseline, with no good effect. In fact, the medications made my lips MUCH worse, but that might have been due to any number of secondary ingredients in such creams.