Well, it seems that you are very interested this question. Anyway, I should tell you that the color of our eyes is decided by our genes type and chromosome type,which could not be changed later in our life. Anyway, there will always be some exceptions in the world, it is possible for someone to have two different eye colors but the cases are really rare.
Well, generally speaking, yes, it happens, but it is rare. It is possible to have different color eyes. And in many cases, there is something to do with the genetic causes of this problem. And also, a blow to the head can damage the tissue that produces brown pigment, making one eye no brown. You should know that the layer of brown pigment covers up other colors, like blue or green. In the absence of the pigment, you can see the underlying color in the damaged eye. So it is common for some people to a blue eye and a green eye. By the way, according to some experts, there is also something to do with the blood passing. Anyway, you can console it with your doctor.
It sounds like hardly worthy of belief, but it's really possible to have two different eye colors. It's an unusual situation named heterochromia. In reality, our eye color is determined by the distribution of pigments. Hence, all the factors which influence this distribution will finally give rise to different eye colors. Professional terms called Binocular Heterochromia and Uniocular Heterochromia. There are two major reasons, one is presented by heredity, and the other stems from environment effects. I can even cite an instance for you. Jane Seymour, American actress, playing a famous role in "Live and Let Die", who have different eye colors, one hazel and one green. Besides, there are more persons who have different eye colors, you can check out online if you have interest.