Cat Scratch Disease: This is a common condition caused by the bacterium Bartonella henselae, transmitted through cat scratches or bites. It typically presents with a lump or swelling in the lymph nodes, often in the armpit, and can be accompanied by systemic symptoms such as fever and swollen, red eyes due to conjunctivitis.

Infectious Mononucleosis: Caused by the Epstein-Barr virus, this condition can lead to lymphadenopathy (swollen lymph nodes), which might be felt as a lump under the arm. It can also cause conjunctivitis, leading to red, swollen eyes.
Lymphadenitis: Inflammation of the lymph nodes due to infection can cause lumps under the arm and, if the infection spreads or is systemic, could lead to symptoms like red, swollen eyes.
Tuberculosis: Although less common, TB can cause lymphadenopathy and systemic symptoms, including eye inflammation.

Lymphoma: Both Hodgkin and non-Hodgkin lymphoma can present with lymphadenopathy, which might be noticed as a lump under the arm. While less common, lymphoma can also lead to systemic symptoms, including eye problems.
Metastatic Cancer: Certain cancers can metastasize to the lymph nodes, causing them to swell. Although rare, this would be a critical diagnosis not to miss, as it significantly affects treatment and prognosis.
Sarcoidosis: An autoimmune disease that can affect multiple parts of the body, including the lymph nodes and eyes, leading to the symptoms described.

Kikuchi-Fujimoto Disease: A rare, self-limiting condition that causes lymphadenopathy, often accompanied by fever and other systemic symptoms. It's more common in young women and can include eye symptoms.
Kimura Disease: A rare, chronic inflammatory disorder that can cause lymphadenopathy and eosinophilia, sometimes accompanied by eye symptoms like conjunctivitis or uveitis.
Castleman Disease: A rare disorder that involves an overgrowth of cells in the lymphatic system, which can cause lymphadenopathy and systemic symptoms, including eye problems.