Thanks for writing to us.
from the description provided i could think of two possibilities.
eczema presents as itchy dry red rash
with peeling or thickening of skin
fungal infection may present as dry itchy skin with possible involvement of nail.
your first doctor thought its fungal infection and gave you an oral and topical antifungal
while your second doctor diagnosed it as eczema.
The best way to diagnose these two conditions is to get a skin scraping done of affected area. The skin scraping can be checked for fungus.
hope that answered your query.