I had a similar problem years ago. I had intense itchy on a small spot on my areola. The skin was flaky and reddened. After about a year of this, I went to my OB/Gyn. She was concerned it was Paget's Disease of the Breast, which is strongly associated with an underlying cancer. Paget's has to be considered when a woman has persistant, localized area of scaly, red, itchy skin on her nipple. I ended up with a mammogram and biopsy, all of which was normal.
In your situation, I would be less worried. The problem has not been going on for very long (versus a year for me). Most Paget's involve the nipple and areola (yours sounds like it farther away than that). Paget's frequently looks like an unhealed wound: oozey, crusty, etc. This doesn't sound like what you are experiencing. It may be that you have a localized area of atopic dermitits, which is what I had, or some other completely beign problem. Also keep in mind that Paget's is extremely rare (it represents 1% or less of all breast CAs) and usually doesn't affect women under 50.
It seems unlikely to be Pagets. Here's some info and links, so you can decide for yourself:
From BreakThoughBreastCancer: Types of Primary Breast Cancer...Paget's disease is a rare form of breast cancer affecting the nipple. Overall it accounts for about 1% of female breast cancer. It is characterised by a red scaly rash on the nipple itself, which may spread to the areola (the darker area around the nipple). In 90% of cases where this eczema-like rash is seen, it indicates an underlying cancer in the breast ducts.
The skin of the nipple may appear crusted, scaly, red, itchy, bloody or ulcerated and a burning sensation may be felt. A lump may also be detected in about half of all cases. If there is no lump, the prognosis for this type of cancer is better.
This type of cancer can be confused with skin conditions such as eczema, dermatitis or psoriasis, making it difficult to diagnose. However the key characteristic here is that the rash usually affects the nipple first and does not go away.
From the National Cancer Institute: Paget’s Disease of the Nipple: Questions and Answers...Symptoms of early Paget’s disease of the nipple include redness and mild scaling and flaking of the nipple skin (1). Early symptoms may cause only mild irritation and may not be enough to prompt a visit to the doctor (3). Improvement in the skin can occur spontaneously, but this should not be taken as a sign that the disease has disappeared. More advanced disease may show more serious destruction of the skin (1). At this stage, the symptoms may include tingling, itching, increased sensitivity, burning, and pain. There may also be discharge from the nipple, and the nipple can appear flattened against the breast (1, 2).
In approximately half of patients with Paget’s disease of the nipple, a lump or mass in the breast can be felt during physical examination (1). In most cases, Paget’s disease of the nipple is initially confined to the nipple, later spreading to the areola or other regions of the breast (1, 2). The areola is the circular area of darker skin that surrounds the nipple. Paget’s disease of the nipple can also be found only on the areola, where it may resemble eczema, a noncancerous itchy red rash (1). Although rare, Paget’s disease of the nipple can occur in both breasts (2)....
From MayoClinic.Com: Paget's disease of the breast...Paget's disease of the breast affects your nipple and its surrounding skin (areola). It's easy to mistake the signs and symptoms for skin irritation (dermatitis) or another noncancerous (benign) skin condition of the nipple. In the early stages of the disease, you might notice only some flaky or scaly skin on your nipple, accompanied by slight itching or redness. These skin changes can come and go, making it appear as if your skin is healing on its own. On average, a woman may experience signs and symptoms for six to eight months before a diagnosis of Paget's disease of the breast is made....
Another kind of breast cancer that affects the skin's appearance and can be itchy is inflammatory breast CA. But with that the skin is red and hot and the breast is swollen, which are things you are not describing. So that seems very unlikely.
I hope all turns out to be fine.