I’ve heard a lot of different opinion My Son has never had tightness nor had any pain. That being said I’ve seen college infielders ice there arms after games precaution or necessity ? My son is 11
The first time I ever iced my arm was when I was 18 and my doctor told me I should to stop the swelling from my tendinitis. What he told me was that if it wasnt sore or hurting, you dont need to ice. So i would just say its a precaution. Just make sure that your son is honest with you about his arm. I would never tell anyone if my arm really hurt and always tell people i was alright if they asked even if i wasnt because I wanted to play the game. It probably wasnt the best thing, but I didnt go to baseball games to watch. At that age you can usually tell though of course.