Oh yeah, definitely bind less for now! You DO NOT want to be coughing with a binder on, it really increases the risk of rib damage.
Or maybe if you have a binder that's a little looser, and doesn't constrict your breathing at all, but still helps maybe switch out to that one for when you have to bind while sick. I have a binder that's slightly too big to be effective at complete compression, but it still helps compared to nothing, and is great for when I need to loosen everything up and give my chest a break.
If you spend a good week or so with minimal binding, and lots of rest you should start to feel better I'd wager. Only thing is remember not to just hop the gun at the first sign of a clear nose, and start binding like you were before you got sick. You wont want to make yourself feel worse again, and you said you bind for like 14 hours a day. That's some rough stuff on your torso.
Take it easy man, and I hope you feel better soon!