Having red or teary eyes is a common side effect of staying up too late or partying too hard. However, if you have woken up and the whites of your eyes have turned red, it can be a signal of a much more serious issue.
Though your eye being a bit bloodshot will usually be no cause for concern, if that redness goes along with any pain or sudden changes to your eyesight - it is important to have it checked by a medical professional.
Some of the conditions that cause your eyes to turn red can be treated with a course of medication like conjunctivitis. However, others can require medical intervention to prevent permanent sight loss - so knowing how to differentiate between these conditions is important.