Penny wise is pound foolish.
Find a competent sports medicine doc, get a second opinion, then follow the wisdom to the T.
Unless your son's entire goal was making the varsity in ninth grade, a kid is playing with fire in playing through any injury. What's the point in getting that extra game in if the potential risk is six months off.
For non-athletes, fighting through the pain of tendonitis may risk little; for the athlete, whose body will "adjust" by changing mechanics to avoid the pain, there is much at risk.
I believe it was one of the Dean brothers (either Daffy or Dizzy) who had been struck on the toe by a line drive and attempted to pitch through it; that changed his throwing motion and caused the shoulder injury which ended his career. (wikipedia)
Injuries are part of the game and kids going through growth spurts are especially vulnerable. Combine that with an environment where kids are "weak" for not gutting it out and a recipe for disaster is served. If college ball is a goal, the process is a marathon; play it like a marathon; dont play it as a sprint AND a marathon.