Depends on the cause. Improvement from redness depends on the cause of the problem in the first place. Redness caused by bleeding on the white of the eye (subconjunctival hemorrhage) may take weeks to disappear, while allergic red eyes can be treated within a few days. Redness is a sign of inflammation, and it is telling you that something needs to be treated. See an eye doctor as soon as possible.
Possibly. Red eyes can come from superficial bleeding, allergy, infection, or inflammatory disease of the inside of the eye. Symptoms requiring evaluation by your ophthalmologist include pain, lowered vision, light sensitivity and pus seeping out from the lids. If none of these are present you probably have subconjunctival hemorrhage or viral infection and can wait several days for clearing.