Pain in big toe mild swelling after falling down stairs. difficulty walking (walking on side of foot). pain wakes me and i think bone is displaced?

See a doctor: An x-ray will show if heir a displaced fracture.Not moving and splinting a fracture prevents further injury.

If you fell: Downstairs and have difficulty walking the foot likely should be xrayed. You also sound like at minimum should be walking in a surgical shoe that prevents the toe and metatatarsal joint from bending. Ice would do you well as well. Good luck.