Hi, I can understand your concern for severe cracking and peeling of left palm and the nail beds. There can be multiple possibilities of the same and it requires a close physical examination to diagnose the exact entity of the problem. In my view correlating with the facts you have provided it appears to be fungal infection of the hand area. I suggest you to meet a dermatologist to for proper therapy. In between you should wash the area properly. If I were your dermatologist then presumptively would have preferred to apply an antifungal cream such as clotrimazole or miconazole along with antifungal tablets. You can take an antihistamine such as loratadine for once a day if itching is present. Do not try to pinch, pop or squeeze the area as it may cause secondary infection of the area. All the best