Do doctors think it's genetically possible for someone to have red eyes?

What part? Iris?: I'm assuming that you are referring to the iris (the color portion -- blue eyes, green eyes...). The short answer is no. People do not have red irides. However, some people are born without irides, which allows the eyes to have a red/orange appearance because the back of the eyes are visible -- like red eyes from night photos when the pupils are dilated.