Pitching with proper mechanics should not produce pain. Why not post a video of your son to check his movement for risk factors. Remember, a hard throw is different from a soft throw, so if you do post one, try to get him to throw hard in the clip.
As long as he’s not in pain, at age 10 you probably want to just lay back a little bit on him. …At any age, the motivation to work on pitching needs to come from the pitcher.
Just make sure that he understands that he needs to be honest about when he’s hurt.
But yeah, I have to agree with some of the other responses: throwing hard in practice is vital. You need to practice exactly what you hope to improve. Momentum Pitching’s creator Dr. Brent Rushall calls it ‘The Principle of Specificity’. That’s why throwing softballs won’t help you pitch. Weighted balls won’t help you. Lifting weights won’t increase your velocity. Towel drills won’t improve your form… High velocity baseball pitchers need to train to pitch baseballs at high velocities.
Another approach to your situation could be for you to design practices in a way that allows you to manage out some of the guesswork here… Consider:
Every practice session should start out with the athlete’s assessment of how he/she feels; physically, mentally, etc…
Bad assessments should indicate a need to reduce the length and perhaps the intensity of the workout
Get your son warmed up and loose
Get him up to his high speeds
Practice at top output until he is finished (at age 10 about 30 pitches) OR until you notice EITHER a drop in speed OR a loss of control.
Once fatigue, soreness or pain or even mental anxiety is involved, any further training will be counterproductive.
Just out of curiosity, how many pitches does your son throw in a normal practice session?