When you are cycling, you'd better wear the protected goggles. Or else, your eyes may get the invisible bacterium in the eyes. That is why your eyes feel hurt. You should use some eye drops with anti-inflammation to make the eyes feel comfortable. Besides this home remedy, you could also use the warm compress to make your eyes feel better.
I guess, you must cycling with naked eyes. If so, it can be normal to feel eyes hurts. When you cycling, there are many particles, flying things, insects that may hurt your eyes. Besides, it will create strong wind when you cycling that also bad for your eyes. It will likely make your eyes red and look even swelling. But, usually, this is not a big problems, have a good rest, you may recover. So, the next time to cycle, please don't forget to buy yourself a pair of cycling goggle.
You may have infections or inflammation, or you are just tired, then the wind makes your eyes more uncomfortable. There's no need to worry, just stop cycling recently. And you should do some home remedies to cure the hurt.
Clean your eyes with pure water to make the dust out, then use some artificial tears to relieve your eyes immediately. Then you may see a doctor the other day if you still feel hurt the other day.
Ok, from what you said, I can feel there must be something wrong with your body. Generally speaking, our eyes would not pain when we take sports. But if we are much too tired or get a lack of sleep, our eyes would have problems. Also, it is likely that you have got some sand into your eyes, so in the future you'd better get a pair of sports goggles to protect your eyes.