Red eyes can be caused by eye infection, inflammation, internal thermal, or tiredness. So you can analyze the reason based on your own situation. Are you tired? Is there any itchy feeling? Can you feel the extra hurt?
If the answers for the latter 2 questions are both yes, you may probably get infection or inflammation. Then you can take it easy if your red eyes just caused by tiredness. No matter what, using artificial tears to relieve your eyes can always helpful.
Well, of course, it will make your eyes become red when you have running. First, you may know that running will just make your blood pressure become high. And in that way, it will also have some influence on your eyes, leading to high eye pressure. And if the situation keeps in a long term, it will just have some symptoms in your eyes, such as red eyes, bloodshot eyes. Also, lack of water during running, can be another reason. So just drink more water. And pay more attention to your eyes.
Sometimes when you run or do some other sports, you blood pressure will get high and the circulation of your blood will increased, it may be some kind normal. But if is very red and very serious, you may have the eye problem of red eye, which is an inflammation or infection of the eyes, so you need to go to see the doctor and have some tests.