Yesterday I fell and stubbed my left big toe. Theres no bruising but at the base of the toe where the nail meets it sometimes hurts to bend it. Sprain?

Possible sprain. Pain may be due to fracture, sprains, arthritis, muscle, nerve or tendon injuries. Have the foot evaluated so that you may get the appropriate care.
Contusion. A sprain would be almost impossible at this level, it is probably a bruise.
INJURY. It just sounds like a contusion but even if it was fractured no treatment is required and it will heal on its own.