Hello. I got several suggestions for you. First, as we all know, sports will make blood-vessel outspread, just like alcohol does. Second, it may also be the reason that the sweat after doing push ups flowing into your eyes.So, your eyes may be fine. But if you feel very uncomfortable and this kind of feeling lasts for a long time, you eyes may get inflammation, you can go to hospital and have a check.
I think this maybe the same causes as people got bloodshot eyes after strength sports activities. And it is possible to get bloodshot eyes after the exercise of push ups because of a number of factors. This is because the extremely exercising of push ups can cause broken blood vessel. If you feel pain and with red eyes, you'd better consult an eye doctor.
Usually, just the sports activities will not cause the bloodshot in the eyes. There must be some other reasons for it. For example not enough rest, conjunctival inflammation of the cornea, hypertension and diabetes may be the incentive reason. That is to say, your eyes are not healthy at the moment. After you have done the pushups, the symptom becomes obvious. You'd better go to see the doctor and have a full check on the eyes.