Too late.

Just please remember to refrain from cursing.
Honestly, I've had some nipple irritation but not to the extent you're talking about. Could you be allergic to something in the binder which is causing such a reaction? I dunno, a dye or something. Just seems odd that you'd be having such issues from compression alone, especially the pealing and all. Unless of course you're causing sever rug burn from the binder scraping against the skin, which it shouldn't do.
Also moving this to the FTM Gear section as it has something to do with binding, and may be of use for other people who may be having similar issues.