There may be many causes for your red eyes. You may get an infection. If it is not very serious, it will go over a few days later. But if you got the pink eye, you may need to see your eye doctor immediately, because there are some kinds of contagious pink eye. Doctor will give you prescription treatments.
You'd better not ignore it, because you don't know what caused your red eyes and whether it is serious or not. If you just have drunk last night and sleep too late, your red eyes may be caused by lack of sleep and alcohol use. Your symptom will disappear a few days later. But if it is caused by some serious disease, ignore the symptom will make you miss the best time treatment and will bring you further inconveniences.