My son is 15 years old and just now is starting to throw curveballs. Should he limit throwing them and how many should be his maximum per day?
You definitely waited until the right age for you son to start throwing this pitch. It is recommended to wait until the child is 15-16 years old before throwing this pitch.
There are very few resources on the web that list the recommended number of pitches a player should throw at this age because everybody is different. But throwing a curve ball at this young of an age is very dangerous if you throw it incorrectly. So you have to be very carful. Throwing a curve ball with bad technique can cause serious elbow injuries.
As long as he is throwing the curve correctly, he can throw as many as he wants. If he complains about any pain or pinching, stop immediately. If you want to play it safe, take the number of pitches (non curves) he usually throws, cut it in half and have him throw that many that day. Do this until he feels perfectly comfortable.
Here is a video that shows the proper way to throw a curveball without causing injury.
I also agree with what wax eagle said. Talk to your doctor. I'm just trying to make a point that if done incorrectly, your son might injure his elbow.