Well, yes, I have to say that it is possible to have red eyes when you have reading. Generally speaking, there are many people who suffer red eyes when they read for a long time. According to some researches, when you have reading, it will just make your eyes focus on the small points for a long time. In that way, definitely, it will increase the eye pressure, leading to eye strain. And then your eyes will feel tired. In many cases, redness in your eyes can occur. For your situation, I will suggest you stop reading, and just have a rest.