Normally inner layer of the
nose nostrils have blood vessels at the extreme outer layer of the skin in the
nose. When we sleep, mucus gets solidified, and in the morning when we try to remove the solidified mucus, this also damages the blood vessels and hence the blood in the mucus. But this lasts only for a moment as the blood vessels are very thin and they get closed either by the clotted blood or by the skin itself.