Fungus is unlikely, because for unknown reasons fungus affects only one hand at a time, in most cases.
Eczema, psoriasis, and skin problems associated with arthritic conditions are all on the possible list. Diagnosis depends on appearance and the presence or absence of other symptoms in the skin or elsewhere.
I recommend setting up an appointment for a second opinion and inquiring about a cancellation list to get seen sooner. Meantime, I would press the first dermatologist about diagnostic suggestions and therapeutic alternatives. (For instance, wrapping the hands in plastic to enhance absorption of the lotion, tar soaks, etc.)
Best.
Dr. Rockoff