I have a dark blue coloring under my eye, and some red streaks on them is this a sign of tiredness?

Probably not much: Dark circles under eyes from lack of sleep is somewhat of a myth. It is much more likely to be caused by heredity, thinner skin there allowing blood vessels to show through, rubbing or scratching eyes, even allergies. Apply a cold compress (bag of frozen peas in clean cloth) to constrict blood vessels. A lack of sleep may cause paleness/hollow-eyed, making shadows and circles more obvious.