You absolutely should discontinue any materials you are allergic to NOW. Thats good advice japdip gave with sports bra, use gause pads and secure with that, and get to a doctor.
I hope that you have seen your Physician about these boils on your breast. If not you should do so as soon as possible. As far as pain med.s; I'm sure your Dr. would advise you as to some over the counter medication OR give you a prescription for something stronger if needed. Now to the tape issue; the only option I can think of is to apply the bandages and wear a very soft sports type bra to hold them in place. i can't see too much relation between these boils and breast cancer but once again your Dr. who has seen and examined you would be the best person to advise you about having a mammogram at a later date. Regards ....