Hello XXXX,
I have read carefully your question. From what and how you have explained above, I agree with your doctor, that the dry lips are unrelated to a
fungal infection, since in general the fungal infection spreads on the mouth mucous with creamy white, slightly raised lesions - usually on your tongue or inner cheeks but also sometimes on the roof of your mouth, gums, tonsils, or back of your throat.
You might know that humidity is the main factor who helps an fungal infection to develop, and the lips are not a common place where it spreads.
If I was your doctor, I would have checked you after 2 weeks time, while you use the local treatment in hands and feet as recommended, and reevaluate if you need to start using oral medicines if worse or not better.
I would not have started oral medicines at this level, since the risks and side effects of using those, are higher then the benefit.
If any more questions, feel free to ask again.
Regards,
Dr.Klarida