It may just caused by the tiredness, and this is the slight problem, you can easily cure that by relax. More serious problem may be infection or inflammation. If your eyes turn red pretty soon when you read books, you need to take it seriously.
By the way, itchy and hurt may occur as the company of the red eyes if your eyes get infection.
You need to stop reading immediately, then clean your eyes with pure water or physiological saline. Use some artificial tears to relive your eyes.
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.
Sorry to hear that, you may get red eye or pink eye if you have such symptoms. And it is an inflammation or infection of the eyes, it can be caused by allergies, bacteria, viruses, or toxic substances. Since your eyes appear red after reading, it may be caused by your eye plus your pink eye. Go to see the doctor and have some suggestions.