My son is suffering from the same kind of thing, except he's a lefty and its his right hand. He's been through X-ray, MRI and diagnosis.
The verdict was ECU tendon instability. Most commonly diagnosed in golfers and tennis players, but not unheard of in baseball players.
We're in a long, long wait period where all he's done is pitch. The original injury was in March and persisted through HS season in mid-May. We got an x-ray (for the hamate bone) in mid-May and it was clear. By the time we got in to the orthopedic surgeon, it was late May, MRI in early June, diagnosis in mid June.
He's resting until August 4th to see if it recovers on its own. He's going through some light physical therapy in the meantime. If it looks good next time, he'll start swinging with a t-ball bat and work up from there.
If not, he'll probably have surgery and try and recover as quickly as possible before the spring HS season.
Anyone else have experience with this kind of injury?