There are a couple different possibilities here, and I would recommend that you go see your primary care doctor
who can take a look and help you figure things out quickly.
One possibility is that this is athlete's foot, which is a fungal infection of the skin of the feet. Athlete's foot symptoms include peeling of the skin, like you are experiencing, as well as itching, cracking, redness, and foot odor. Fortunately, most of the time athlete's foot can be easily cured by using good skin hygiene and by applying a topical anti fungal cream, some of which are over the counter.
Another possibility would be dyshidrotic eczema
, which causes small blisters to form on the bottoms of the feet, which eventually coalesce, causing peeling of the skin. There is often severe itching, and the skin may be reddened and irritated looking. Dyshidrotic eczema can generally be treated by the use of high quality skin moisturizers, together with prescription strength topical steroid creams, as prescribed by your doctor.
Start by making an appointment with your doctor as soon as possible. They will be able to help decide which of these conditions you might have and which medications are best to use.