As a matter of fact, I am also crazy over cycling for I find it really amazing and could relieve me of my stress from work and study. Anyway, cycling or driving, would not have serious impacts on your eyes, except that sometimes sand or dirt could get into your eyes, leading to some slight problems. Therefore, it would be wise for you to wear some protection glasses. As to your problem, I think it is due to a lack of sleep or improper use of your eyes, which requires some medical checkup in the hospital.
When you are cycling and not wear the protected goggles, your eyes will be stimulated fast with the high speed which will cause them get the invisible bacterium and get the infection. Thus, you'd better wear the protected goggles to prevent your eyes from the wind. You could also not drive too fast which will not be safe too.