Cat Scratch Disease (CSD): Given the recent exposure to new kittens and the development of upper extremity lesions, CSD is a strong consideration. The disease often presents with lymphadenopathy (enlarged lymph nodes), which can be tender to touch, and systemic symptoms like headaches. The lack of response to amoxicillin also supports this diagnosis, as CSD is typically caused by Bartonella henselae, which may not respond to beta-lactam antibiotics like amoxicillin.

Streptococcal Pharyngitis: Although the patient did not respond to amoxicillin, it's possible that the dose or duration was insufficient, or the infection could be caused by a resistant strain. The presence of a neck lump (potentially a lymph node) and headaches could be consistent with a severe pharyngitis.
Viral Pharyngitis: Similar to streptococcal pharyngitis, viral causes could lead to lymphadenopathy and systemic symptoms like headaches. The absence of response to amoxicillin would support a viral etiology.
Toxoplasmosis: Given the exposure to kittens, toxoplasmosis is a consideration, especially if the patient is immunocompromised. However, it typically presents with more systemic symptoms and less commonly with localized lymphadenopathy.

Lymphoma: Although less likely, lymphoma could present with lymphadenopathy that is tender to touch and systemic symptoms like headaches. It's crucial to consider and rule out malignancies due to their significant implications.
Tuberculosis (TB): TB can cause lymphadenopathy and systemic symptoms. Given the potential for severe consequences if missed, TB should be considered, especially if the patient has risk factors for exposure.
HIV: Acute HIV infection can present with lymphadenopathy, systemic symptoms, and might not respond to typical antibiotic treatments. Given the potential for severe consequences, HIV testing should be considered.

Kawasaki Disease: Although more common in children, Kawasaki disease can present with lymphadenopathy, fever, and systemic symptoms. It's a rare but important consideration due to its potential to cause cardiac complications.
Brucellosis: If the patient has been exposed to animals or their products (e.g., unpasteurized dairy), brucellosis could be a rare cause of lymphadenopathy and systemic symptoms.
Leptospirosis: This zoonotic infection can cause a wide range of symptoms, including lymphadenopathy and headaches, especially in individuals exposed to water or soil contaminated with the urine of infected animals.