There are many eye problems you get when you breathe that causes your eyes get hurt. You may get the eye infection because of the invisible bacterium. You may let the eyes get inflammation which cause the eyes get red. You may get the eyes blood shot when you breathe. Under normal circumstances, conjunctival blood vessels are flat which is in a deep sleep state. The intravascular does not have the blood through. That is why the sclera always appears that white. When bacteria and virus invasion come under your unconscious state, your sleeping blood vessels will soon expand. The red blood will cover the surface of the eyes. The sclera is red up. Inflammation of the eyes is the most striking symptom, with quick, chronic conjunctivitis, all kinds of keratitis, iridocyclitis, scleritis, glaucoma which have the different degree of eye congestion. You'd better go to see the doctor and find the eyes problems. Then you could treat it.
It seems that there is something wrong with your eyes. Because generally speaking, our eyes would not simply hurt while we are breathing. Anyway, it might be resulted from some slight problems, maybe an eye strain or fatigue. Whatever you suffer, you should visit a doctor and take measures to tackle the problem, because it could be seen as a sign of eye problem.