You definitely need to see the doctor if this persists more than a week or two.  You have already tried the most logical home remedies without any effect.  A scaly rash in the nipple area can be a symptom of a type of cancer called Paget's Disease of the Breast, and swelling can be an early symptom of inflammatory breast cancer.  Your symptoms could also just be related to some hormonal changes, so if getting a doctor's appointment is difficult for you, you could wait and see if all of this goes away after your period.  Breasts often swell and itch before a period, and sometimes that swelling isn't even on both sides.  Your initial guess that this is a fungal infection could also be on track, and the doctor might have a better, prescription strength cream for it.  So I don't think you need to panic, but I do think you need to stay on top of this and find out what is causing your symptoms.