Hi Reese!
Binders can be a such a pain. I have a some suggestions that may help:
1) Wear a soft vest underneath you binder.
2) You know that bra padding you can get at sewing shops? Position one of those in each of the armscyes. If it helps you could sew it in permanently
3) try different positioning of the binder. Try wearing it a bit higher or lower than you normally would see if that helps.
That's all I can think of right now. I'll add more if anything comes to me. Hope it helps a little, good luck <3