I have a red blood spot on my eye? Should I see a doctor?

Bleed. This is a sub-conjunctival hemorrhage. As long as the vision is unchanged and there is no pain, everything should be fine. If it is a little irritated, then you can use an artificial tear up to 4 times a day to lubricate. This is due to a blood vessel leaking blood and is usually without cause. Sometimes straining or blood thinner can cause this. If it continues to happen, follow up with eye md.
Not necessarily. A small blood spot - bright red - just under the surface of the eye is usually a subconjunctival hemorrhage due to a small broken vessel - this happens sometimes with a cough - or sometimes from minor trauma. It resolves on its own without treatment.