In my opinion the rash
seems to be either eczema
( if affecting both sides ) OR fungal skin infection
which will not get better completely with local anti biotics as you will need a cream that has mild steroid+ anti fungal agents.
have you got any nipple discharge
You will need the breast examination done by Dr as well to rule out any possible breast lump as in few rare cases a form of breast cancer
can present as itchy rash non nipples which is not healing with creams used to treat common skin infections - I suggest you book appointment with Dr to have full examination done - also it may have further implications if you are in certain age group & if there is any family history of cancer.