First, it depends on your age. I started taking advil in college in moderation. After a few shoulder operations I moved on to some stronger pain killers which you would need to be very careful of.
Unfortunately, I needed the pain killers to get though an outing as my arm deteriorated. Just try not to become dependent on anything.
For teenage pitchers, I recommend icing consistently, and light weight training between starts to help with a quicker recovery.