Yes. Cold sores are caused by the herpes virus and occur on any mucous membrane; that is, the mouth, nose, eyes and genitalia. They are most common in or around the mouth.
Sores. Depending on what is causing sores they can occur many other places. Cold sores can be on or around the lips, even elsewhere on the face. If they are near the eye you should see your doctor! other types of sores like in hand-foot-mouth can occur on their hands and feet and even bottom!