Can a foot injury called sesamoiditis go away on it's own, and how?

Yes: Best to rest the area by wearing a pad that off loads the pressure.

Rest and offload: Rest will help. More supportive shoes with cushion will help as well. Padding or offloading sesamoids will limit stress and tension to allow healing. If a prolonged problem, see podiatrist.

Yes, by taking : Pressure off the sesamoids. There are pads called dancers pads that do just that. An alternative would be a custom made orthotic. Stay away from heels while you have this condition.