How long can I wait with red eyes to see if it goes away without seeing a doctor?

Depends. 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.