Hello~I would say that you probably dislocated it a little as you were picking up speed to cross the street. I would put on alternating cold and hot packs on the area for a day or two, each for approximately 15 minutes, do this 3 or 4 times a day, and, if it doesn't improve see a podiatrist. It is more than likely nothing to worry about, in fact, it could even be a minor spasm that doesn't want to release.
What about trying an anti inflammatory like ibuprofen? That would perhaps give you a little comfort and reduce any internal swelling, relieve any pain. You may have just jammed it without knowing. Also, check your shoes. The biggest issue for toe pain are our shoes. Having shoes with plenty of room for toes is important. If it gets bad, a corticosteroid shot for the toe will help most likely. Here's some information on this type of arthritis in the toe or stiff toe. https://my.clevelandclinic.org/health/diseases/14665-hallux-rigidus