Your symptom is fairly common. There are a few possible causes which could describe exactly what you are experiencing. I would strongly recommend you see your doctor
. The different causes have different treatments and therefore require your primary care doctor
to diagnose it.
The most common cause of what you are describing is Xerosis or dry skin. Especially in the winter, the dry environment causes water to leach out of your skin which results in a dry layer on top. Normally, flaking white skin that is often itchy is a classic description for xerosis. The hands and feet, which are most exposed to the environment, are common locations. The cortisone you have taken will not help xerosis, and will likely worsen it as it can thin out skin. Moisturizing lotions like Eucerin are more beneficial.
Infections can affect the skin. Bacterial infections are normally red, warm and tender. Fungal infections can give the flaky skin your are describing. It is less likely (although possible) to be a fungal infection as being on both feet and both hands would be rare.
Primary skin conditions like psoriasis
or atopic dermatitis can also cause this. Allergies are normally itchy, red areas. This would be less likely. Please talk to your doctor.