Personally, I think you should only do it if you are hurting or have pain. My son generally does not ice. Only once in a while when he tells me his arm is "hurting". He will get "sore" when he goes into the 90's in pitch count, but we don't even ice him then. I think you should be "sore" when throwing that many pitches. The other night he threw 3 innings on 3 days rest (Monday outing, then Friday outing) after going a complete game - 7 innings 67 pitches - and he said his arm was "hurting". We iced that night. Went 20 minutes with ice, about 30 minutes without and 20 more with ice. Next day he was fine.
Son is pretty good at letting me know the situation. When he differentiates between being "sore" and "hurting" I will opt for the ice just to be safe.
By the way, the hurting was a generalized hurting in the upper arm. Nothing in either the elbow or shoulder joint.
Bottom line is, if there is any pain or anything more than general muscle soreness, ice. That is always the way we have dealt with it.