During the winter, a small part of areola dried and got flaky. That wound has not healed since two months. There is no pain and lump in either breast?

Need Biopsy. Any time a sore or skin leision lasts more than a couple of weeks, esp on your breast, it should be evaluated and most likely you should have a biopsy. Many causes of this some serious some not so much, I'm worried about Paget's disease .