How do I get rid of large popped red vessels in whites of my eyes?

Just wait. If you are referring to a subconjunctival hemorrhage, or "broken blood vessel", there is really nothing to do to make them go away faster. Usually takes between 4-10 days to resolve. If you get repeated broken blood vessels, the blood pressure and blood clotting parameters can be checked. The hemorrhages will not affect your vision.
Time, usually. If you are referring to a red patch of blood on the white part of the eye, known as a subconjunctival hemorrhage, or "bloodshot eye", then only the passage of time is necessary. Most turn orange, then yellow, and disappear in a week or 10 days. No drops or surgery are needed. Repeated hemorrhages may indicate underlying body diseases, like clotting disorders, and should be checked out further.