I have a non-union break of the sesamoid bone which threw me off the exercise wagon for several months. The podiatrist did give me orthopaedic inserts to wear for 6 weeks and this greatly improved the discomfort. I am back to wearing heels after 3 months and just ran for the first time again last night.
I was told that mine was an overuse injury - I was training for a triathlon but had to drop out because of the break and just 3 weeks before the triathlon too.
I'm taking the running slowly now since the podiatrist didn't give me good odds of it healing without surgery, however, that is a broken sesamoid (confirmed by x-rays) and not sesamoiditis.
I did a lot of research when I first found out and was absolutely devastated but things are improving.
I was told that I could continue swimming and biking as long as there was not pressure or impact on the ball of the foot - this is not easy with biking.
So if you have access to a pool, swimming might be a good option with little impact on the sesamoid.
I wish you the best and a fast recovery.