Hi,
Skin problems can occur on the breast like on any other part on the body.
If you haven't noticed any abnormal features on breast self examination like rapid breast swelling,redness,nipple discharge,or have a sores that won't heal,then it's more likely a skin problem,like dermatitis or an allergic reaction of some sort,due to a new soap,scratchy clothing or any new products that you might be using.It could also be hormonal or caused by some type of medication you are taking.
Try not to scratch the itchy area,because the more you do, the more it will itch.Wear a cotton material bra,apply calamine lotion and take some oral antihistamine medications for the itching and see if it helps.But if it persists,my advice to you would be to consult a dermatologist or your health care provider to get a proper clinical evaluation.
Best wishes ..