There are a couple possibilities. By far the most likely is that you are developing athlete's foot. This is a fungal infection of the skin on the feet, and it is very common in people in college, especially if they live in shared housing, as the fungus is often picked up in bathrooms or shower stalls. Athlete's foot causes cracking, peeling, and itching of the feet, and there is sometimes an odor. Fortunately most cases can be fairly easily treated with an over the counter antifungal cream, available from your local pharmacy.
Another possibility would be eczema
, an inflammation of the skin causes by a range of factors, including a person's individual skin sensitivity and exposure to irritating or allergic substances. Eczema typically causes dryness and itching of the skin, but can also manifest as peeling of the palms or feet and it is often worse in stressful times (such as college).
, an autoimmune condition of the skin, can manifest primarily as flaking and scaling of the palms or feet at as well.
I recommend talking to your primary care doctor
, who can diagnose what is going on and help you decide of treatment is needed.