Yes, the yellow eye is a sign of liver damage. When your whites part of the eye become yellow, you should take notice of it. You should go to the hospital to check on the liver part to see whether it has the problems. You should take it into serious care. If there is problem for your liver, you should accept the treatment as soon as possible.
Yellow eyes are a sign of liver problem indeed. I once had acute icterohepatitis when I was a little child. I got fever again and again during that time and find no other reasons which would led to the high temperature. My doctor found that the white of my eyes was very yellowish. So she asked me to have a blood test. From the result of the blood test, they told me that I had acute icterohepatitis. I had to spend one month in hospital to get cured. Usually, if there is some problem with liver, people will look yellowish, not only the white of eyes but also the skin. People usually lose weight and don't want to eat anything, and always vomit. Liver problem could be very serious. I suggest you to see a doctor. Hope you could get well soon.
Well, so sorry to hear that some parts of your eyes are turning yellow. Anyway, it is not very serious in the first place. However, it is not to be underestimated, because it could be a sign of some other problems, including your liver. A lot of problems could lead to yellow spots in the eyes. So, what you should do is to take a medical examination to see where went wrong before it is too late.