Cat Scratch Disease (Bartonellosis): This condition is caused by a scratch or bite from a cat infected with Bartonella henselae. It often presents with a painful lymph node, typically in the axilla, without significant erythema or fluctuance, matching the patient's symptoms.

Axillary Lymphadenitis: Inflammation of the lymph nodes in the armpit can be caused by various factors, including infections, and can present with tender lymph nodes without signs of cellulitis or abscess.
Folliculitis or Furuncle: Although less likely given the lack of erythema, these conditions involve inflammation of the hair follicles and can sometimes present with tender lumps under the arm.
Lipoma or Other Benign Tumors: While typically painless, a lipoma or other benign tumors could potentially cause discomfort if they become large enough to irritate surrounding tissues or if they become inflamed.

Breast Cancer with Axillary Lymph Node Involvement: Although rare in young women, breast cancer can present with axillary lymphadenopathy as the first sign. It's crucial to consider this diagnosis, especially if there's a family history or other risk factors.
Lymphoma: Both Hodgkin and non-Hodgkin lymphoma can present with lymphadenopathy, which may be painful. Given the potential severity of this diagnosis, it should not be overlooked.
Tuberculosis (TB): TB can cause lymphadenitis, which might present with painful lymph nodes without significant other symptoms. This diagnosis is particularly important to consider in individuals with risk factors for TB exposure.

Kikuchi-Fujimoto Disease: A rare, self-limiting condition that causes lymphadenitis, typically in the neck but can occur in the axilla. It's more common in young women and can mimic other conditions.
Kimura Disease: A chronic inflammatory disorder that can cause lymphadenopathy and eosinophilia. It's rare and more commonly seen in Asian males but should be considered in the differential diagnosis of axillary lymphadenopathy.
Castleman Disease: A rare disorder that involves an overgrowth of cells in the lymphatic system, which can cause lymphadenopathy. It's essential to consider this diagnosis due to its potential for significant morbidity if not treated appropriately.