My son is also a catcher and a pitcher. I think the answer you got from Coach2709 is pretty much what my son has done. Based on a suggestion my son got to a question at an excellent college camp, he presented it in a way like this to his coach: I enjoy catching and pitching, but I know I will not be at my best if I try to do both on the same day or on back to back days. Where do you see my highest need to the team? The coach told him the team had more of a need at catcher, so my son said he will then focus on catching during the season. It worked well, and there has been no problems whatsoever.
Now if your son has a similar conversation with his coach and he still tries to catch and pitch him on the same day, then your son can always say his arm is sore. If the coach still insists on using him both ways after he tells him that, then I think you need to request a private meeting with the coach immediately.
Those of us with kids who both catch and pitch live on the edge. These are kids who typically have strong arms and coaches want to take maximum advantage of those arms. However, I read somewhere that the highest correlation the experts have found with players needing Tommy John at an early age are players who both caught and pitched in the same week throughout the season. Most coaches understand this risk and put the players' interest first. But some of these high schools have coaches who need to be told by their players that they should only do one or the other. Hopefully they respect the player's willingness to address the issue with them.