Answer:
The medical term is Subconjunctival hemorrhage. The eye has a red spot of blood on the sclera (the white part of the eye). This occurs when there is a rupture of a small blood vessel on the surface of the eye. The area of redness may be fairly large, and its appearance is sometimes alarming. It is vivid red because the sclera is so rich in oxygen. It is not dangerous and generally goes away slowly with no treatment.
I've had 3 or 4 blood spots in my eye over the past few years, so I went to my doctor to check it out. He asked if I had been lifting heavy object: Yes. Have I been sneezing a lot: Yes.
He found nothing wrong; he just said that I must have a weak blood vessel in my eye - nothing to be too concerned about. Apparently, anemia may have something to do with it too. I usually have plenty of energy, but I have had a blood test or two (over my 47 years) that have come back stating bounder line anemia.
The blood spots in my eyeballs last a week or two.