It really sound strange that the eyes may bloodshot when you sleeping too much. I think it not real. Relax and sound sleep is important for your fatigue body's recovery. However, the excessive sleep will lead you to doldrums and lack of energy. The hour of sleep is not so important but the quality of sleep is the most important factor. The eyes would get bloodshot just by lack of sleep and lack of blood circulation, but no study shows that it would get by excessive sleep. Hope you understand!
Well, yes, it is possible to have bloodshot eyes when you sleep too much, which can lead to eye strain. When your eyes become bloodshot, it means that the tiny blood vessels inside the eyeballs contain too much blood and they are inflamed. And this condition can be caused by high blood pressure. And generally speaking, if you sleep too much, that can be possible to cause high eye pressure. And then it will lead to blood shot eyes. For your situation, you can just have some ice on your eyes.
Bloodshot eyes could be derived from a lot of causes, such as bad use of your eyes, a lack of sleep, or some infections. However, it is rare that bloodshot eyes could be resulted from too much sleep, perhaps it is possible for your eyes would not get good blood circulation. But too much sleep could also give rise to a lot of problems, then you'd better control your sleeping hours and make good use of your eyes, try to get more vitamins and a better diet.