It sounds like what you have is called a pinguecula. This is a change in the skin around the eye (conjunctiva) from a lifetime's worth of exposure to sunlight. It is not a cancer. It also can become irritated and red at times.
Here is a picture of a small pinguecula. You can find many other pictures by going to Google images:
This is a pterygium
. As you can see one of the major differences between a pterygium and a pinguecula
is that a pterygium grows across the clear part of your eye (cornea):
Full Size Image
If you are bothered by your pinguecula it can be surgically removed fairly easily by your ophthalmologist
using local anesthesia. One word of caution however.....they have the nasty habit of growing back, sometimes with a vengeance.
What can you do about your pinguecula short of having it surgically removed? Well, to decrease the redness use soothing natural tears 4 to 6x/day or more, cool compresses and treat any underlying blepharitis
you may have. Drops that “get the red out”, such as visine, will tend to irritate things in the long run and just make the pinguecula redder. These drops, however, are OK to use once or twice to make your eyes briefly look better for a photo or a business meeting but should otherwise be avoided.