Your trainer was both right and wrong (you knew about the wrong). Throwing athletes are always going to have more external rotation on the throwing side vs non-throwing as well as less internal rotation on the throwing side. Getting it to be equal is usually a fruitless task, as your trainer probably knew, but you must push to maximize internal rotation on the throwing arm.
Shoulder pain is the least of it, this type of thing leads to labrum tear, which is the hands down worst injury for a pitcher anymore. I too learned this the hard way...once I did fix the internal rotation, it was too late.