Dry eyes. Most likely you are getting dry eyes. When we read, we stare and do not blink as often. Our tears will evaporate and unless we blink and flush new tears over our eyes, they will get very dry. Try using over the counter artificial tears. Main difference is how thick or thin they are. If tears still do not help, you may need to see and eye doctor to see about other treatment options.
Possibly. This symptom can indeed be a sign of dry eye syndrome. The symptoms often worsen when reading because the blink rate is less when concentrating. Symptoms are also worse in the winter months, during "heating season" as the indoor air is drier then. Symptoms can also be "eyestrain", from an uncorrected refractive error, or eye muscle misalignement. See an eye md for diagnosis and recommendations.