Sounds like your doctor has given you good advice. My son had the same scenario...his ortho gave him a rest and rehab program. Only after that didn't resolve the issue did he suggest an MRI (as well as x-ray). The MRI showed no tears, but a bone spur and some instability. Again, he prescribed conservative rehab approach. Finally, when this didn't resolve it, he decided TJ was the best option (he has done hundreds for many athletes (amateur and professional) and consulted with major league teams). He suggested TJ not so much for the instability, but stating that (1) bone spurs, once removed, often lead to further instability and eventually, TJ surgery, and (2) the bone spurs are evidence of instability.
When he went into my son's elbow, he found the bone spurs not to be as bad as he thought and that the ligament had 3 tears that had probably been there for a few years.
My son is now 8 months post-surgery (throwing off the mound at about 75% and pain-free for the first time in years). Obviously, if he had the MRI and surgery earlier, he would be ready to go now. However, I appreciate our ortho's (and it sounds like your ortho's process) non-invasive approach first.
Good luck to your son. He needs to be patient and take each step as they come (my that sounds trite, but it's true).