I've always bound, starting back when I would use evil Ace Bandages as a kid, with my binding item worn over a cheap plain white T-shirt. It keeps tight things from biting into the skin and leaving cuts/scrapes or showing ugly lines under your shirt.
I'm not sure that would be enough padding for you, but you could try it. It keeps your binders clean too. If you don't like a T-shirt, some guys use tank tops, but the positioning could be trickier if your shoulder is the issue.