Hi. I'm online and happy to answer your question today.
First, the dizzy feeling when you get up too fast could be related to your blood pressure. This should be evaluated by your internal medicine doctor.
Getting back to your eye, you may have a pinguecula.
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 link to a picture of a small pinguecula. You can find many other pictures by going to Google images:
This is link to a picture of 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):
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.
Does this make sense to you?
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