The skin under my fingernails is always swollen and it is pilling what could be the reason ?

Many things: it could be oxygenation problem like clubbing or could be calcium or vitamin D deficiency or fungus infection without looking hard to help go and see a doctor

Many possibilities: Peeling skin around the finger nails can be due to various causes. Some of these include: dry skin, low-grade fungal infection, contact dermatitis from sensitivity to chemicals or nail polish. If the problem is persistent the patient should see a dermatologist.