My 3 month old daughter woke up yesterday with a blood red spot in the inner corner of her eye. Her doctor can't see her until next week.

Harmless. Generally speaking, the sudden appearance of a blood red spot on the white of the eye(sclera) is due to harmless bleeding from very tiny blood vessels that cross the surface of the sclera.Minor rubbing of the eye can cause them to bleed,but the blood is trapped between the sclera and a transparent film of tissue called the conjunctiva (think plastic Saran wrap)>eye turns red. No Rx needed.