You are describing two different problems: 1 redness of the eyes. There are so many causes of this that I cannot offer any specific cause. If it persists see an ophthalmologist or optometrist 2. a white ring around the "iris" actually its usually on the cornea and is called an arcus. If you are 65 or over its usually a normal part of the eye aging and does not affect vision. If younger than that it can be associated with elevated cholesterol and triglycerides and your family MD needs to do "Fasting lipid profile" I suggest you see Eye MD ophthalmologist to deal with both problems.