Can't say I've ever experienced a binder hurting, and I go for the real tight ones. That said I tend to wear something under it as well, of the same material, typically Lycra stuff, so that there's no chafing on the chest. I've never experienced any chafing, it's just that I'm so anal about being flat I'll take several layers. Habit.
If it hurts to breathe that isn't good. You might be wearing something that's just way too small. Or possibly you need to break a new binder in a bit, they do stretch out some after a few uses. Shouldn't affect your ability to eat unless you're planning on eating a huge meal.