If you don't wear the protected goggles, you will easily get the dry eyes after cycling because of the air stream. Your dry eyes may easily get the infection. You could use the eye drops to moisture the eyes. You could also use the warm compress to make the eyes feel comfortable. You could follow the above ways to treat it.
Usually, dry eyes after cycling are caused by wind created by cycling that accelerate the water evaporation in your eyes. So, it shall be temporary and won't trouble your too long. After cycling, you can use eye drops to moist your eyes so as to release your dry eyes. Besides, blink more and take a rest. If you want to keep eye healthy, you'd better take good eye protection during cycling rather than treat it after the cycling. So, just bought a pair of cycling goggles for your eyes to shield wind, sand, insects and particles in the air.
All right, sounds like you are fond of cycling. Actually, I like it , too, for cycling is exciting and healthy. Anyway, it would be uncommon for a man to get dry eyes because of that sports. Perhaps your eye problem is due to some other reasons. Anyway, now you should try to get some eye drops, have healthier foods, get adequate sleep, and try to cry if possible. If the situation is pretty bad, you could also consult a doctor and take some medicines.