Hidradenitis Suppurativa (HS): This condition is characterized by recurrent, painful cysts and abscesses in the apocrine-gland-bearing areas of the body, such as the axillae. The patient's report of a cyst in the armpit that started three months ago, is recurrent after squeezing, and has smelly drainage is highly suggestive of HS.

Infected Epidermoid Cyst: These cysts can become infected, leading to symptoms similar to those described by the patient, including drainage and a foul odor.
Furuncle or Carbuncle: A furuncle (boil) or carbuncle (a group of boils) can present as a painful, draining cyst in the axilla, especially if caused by Staphylococcus aureus.
Cystic Hygroma: Although more common in children, a cystic hygroma (a type of lymphatic malformation) can present in adults as a cystic mass in the axilla.

Lymphoma: Although rare, lymphoma can present with axillary lymphadenopathy that might be mistaken for a cyst. It's crucial to consider this diagnosis, especially if the patient has systemic symptoms like weight loss or fever.
Tuberculosis: TB can cause axillary lymphadenitis, which might be confused with a cyst. This diagnosis is particularly important to consider in patients with risk factors for TB.
Cat-Scratch Disease: Caused by Bartonella henselae, this condition can lead to lymphadenopathy, often in the axilla, following a cat scratch or bite.

Branchial Cleft Cyst: These congenital anomalies can present as cysts in the neck or, less commonly, in the axilla.
Dermoid Cyst: Although typically found on the scalp, face, or neck, dermoid cysts can rarely occur in the axilla.
Axillary Sweat Gland Tumor: Benign or malignant tumors of the sweat glands in the axilla are rare and could present as a cystic mass.