If you think that your eyes are turning yellow, then this is a medical emergency and you need to seek immediate help, either from your primary care doctor
or from an emergency room.
I say this because yellow eyes, known as icterus in medical terminology, are a sign that you have elevated levels of bilirubin in your blood, until proven otherwise. Although occasionally, a darkening of the white part of the eyes, especially in people with darker skin, can be confused for yellowing of the eyes, the assumption should always be that this is a serious problem until proven otherwise.
There are many different causes of elevated bilirubin in the blood stream, but all of them require medical evaluation and treatment. You are right that one major cause is liver problems of one sort or another. Other problems that can cause elevated bilirubin include a blockage to bile flow (for example, gallstones) as well as increased breakdown of red blood cells.
Your doctor will perform a complete physical examination and they will also want to obtain basic blood work to look at your liver and kidney function, look for elevated bilirubin, and look for evidence of breakdown of red blood cells.