Well first I’m sorry your foot hurts. Pain in that area is a problem for sure.
Did you have a specific memorable injury of moderate or greater severity. If not that sure looks like a bipartite lateral sesamoid to me. The lateral one is more likely to be bi or multipartite. Fractures require a significant amount of trauma and I have never seen a stress fracture of the lateral sesamoid (I do not have many runners in my practice however)
You might have either pain at the bipartite junction or sesamoiditis/sesamoid articulation arthritis. An alternative but less common diagnosis is adductor tendinitis but that is far more common in dancers and presents differently.
Unfortunately all of these are hard to treat. Yes. You can try enforced rest in a cast or air cast. If that doesn’t work sometimes shockwave ultrasound will work for bipartite sesamoid junction pain I often will inject w corticosteroid but ironically an injection of the MTP joint will have a positive effect potentially for all of these
Sesamoid excision is a last resort and both should be removed to avoid deviation of the toe afterwards Recovery from this is 3- 6 months.
Am MRI may help now but very specific questions have to be asked. A bone scan may also be helpful and most are combined with a Spect CT scan which has made the bone scan a lot more specific
Best of luck