Although skin cancer is always a possibility with things like this (especially when we haven't seen the spot and are only going on a description), it sounds more like eczema to me, (aka. dermatitis). They usually itch, but sometimes they don't. If it it eczema, it's not contagious or serious, although it can be uncomfortable. Keep the area moisturized with hypoallergenic cream or lotion. It's probably caused by contact with something you are allergic to, so avoid any non-hypoallergenic soaps, lotions, etc.
Regardless, you should see your doctor (maybe even a dermatologist if it's particularly bad) to have it checked out.