Costochondritis: This condition, also known as Tietze's syndrome, involves inflammation of the cartilage that connects the ribs to the breastbone. It can cause sharp pains or aching in the chest that may radiate to the nipple area, fitting the patient's symptoms of intermittent left radiating pain from inside of the left breast to the nipple.

Musculoskeletal Pain: Strain or injury to the muscles or ligaments in the chest wall could cause pain that radiates to the nipple area, especially if the pain is exacerbated by movement or deep breathing.
Gastroesophageal Reflux Disease (GERD): GERD can cause chest pain that may radiate and could potentially be referred to the breast or nipple area, especially if the pain occurs after eating or at night.
Breast Cyst or Fibrocystic Changes: These are common breast conditions that can cause intermittent pain, which might radiate to the nipple.

Acute Coronary Syndrome (ACS): Although less common in women, especially without traditional risk factors, ACS (including myocardial infarction) can present with atypical chest pain, including pain that radiates to the chest wall or breast area. It's crucial to consider this diagnosis due to its high mortality if missed.
Pulmonary Embolism: This condition can cause sudden onset of chest pain that may radiate and could be mistaken for other causes of chest pain. It's a medical emergency that requires immediate attention.
Breast Cancer: While less likely to present with pain as the primary symptom, certain types of breast cancer (like inflammatory breast cancer) can cause pain and should be considered, especially in a postmenopausal woman.

Neuroma or Nerve Entrapment: A neuroma or nerve entrapment in the chest wall could potentially cause radiating pain to the nipple area, though this would be less common.
Sickle Cell Crisis: In patients with sickle cell disease, a crisis can cause severe pain episodes, including chest pain that might radiate in an atypical manner.
Tietze's Syndrome Variants: While costochondritis is more common, other inflammatory conditions affecting the chest wall could cause similar symptoms, though they are less frequently encountered.