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Mehmet Oz, MD, Cardiology, answeredSkin becomes sore and swollen around a cut as a result of inflammation, which is the body's natural defense against injuries. When your skin is cut or wounded, you are at increased risk for infection from bacteria. Your body responds by sending white blood cells to the site of the wound, which destroy bacteria. This produces the symptoms of inflammation, including redness, swelling, and pain. Although it may not be very pleasant, inflammation is a healthy response to an injury.