Costochondritis: This condition is characterized by inflammation of the cartilage that connects the ribs to the breastbone, often presenting as a dull, nagging pain. The patient's history of a recent upper respiratory infection (URI) with a harsh cough, which has since resolved, and the description of the pain being under her left breast, supports this diagnosis. The chronic nature of the pain over several weeks also aligns with costochondritis, which can be exacerbated by coughing.

Musculoskeletal Strain: Given the patient's recent history of a harsh cough, it's plausible that she strained the muscles between her ribs or in her chest wall, leading to the persistent pain.
Post-Viral Syndrome: Some patients may experience prolonged symptoms, including chest pain, after a viral illness due to inflammation or fatigue of the muscles and bones in the chest area.
Gastroesophageal Reflux Disease (GERD): Although the patient denies upper abdominal pain, GERD can sometimes present with chest pain, especially if the pain is worsened by lying down or eating certain foods. However, the lack of typical GERD symptoms makes this less likely.

Pulmonary Embolism (PE): Although the patient denies shortness of breath and other typical symptoms of PE, this condition can sometimes present atypically, especially in younger patients. It's crucial to consider PE due to its high mortality rate if missed.
Myocardial Infarction (MI): While less common in younger individuals without risk factors, MI can present with atypical chest pain. The absence of radiation, upper chest pain, or other cardiac symptoms does not entirely rule out MI, especially in women, who may have more atypical presentations.
Pneumonia or Lung Abscess: Although the harsh cough resolved, it's possible for a complication like a lung abscess to develop, causing persistent chest pain.

Tietze's Syndrome: A rare condition similar to costochondritis but involves the inflammation of the cartilages and surrounding tissues, leading to chest pain.
Sickle Cell Crisis: In patients with sickle cell disease, a crisis can cause chest pain due to vaso-occlusion in the lungs or chest wall.
Thoracic Outlet Syndrome: Compression of the nerves or blood vessels between the collarbone and first rib can cause chest pain, among other symptoms, but this is less likely given the patient's presentation.