Lymphadenitis due to insect or spider bite: The patient's history of being in the garden and experiencing superficial bites, followed by the development of enlarged lymph nodes in the left axilla, suggests a reaction to an insect or spider bite. The absence of fever and the presence of nausea and vomiting, along with elevated liver enzymes (ALT and ALP), could be indicative of a systemic response to the bite.

Cellulitis or abscess: Although the patient mentions superficial bites, there's a possibility of a more serious skin infection that could lead to lymphadenopathy. The elevated liver enzymes could be a sign of a systemic infection.
Viral hepatitis: The elevated ALT and ALP could suggest a viral hepatitis infection, which might not be directly related to the bites but could be a coincidental finding. However, the absence of fever and the specific context of recent bites make this less likely.
Allergic reaction: An allergic reaction to the bites could cause lymphadenopathy, nausea, vomiting, and elevated liver enzymes due to a systemic allergic response.

Cat-scratch disease (Bartonella henselae infection): Despite the patient denying any history of cat scratches, it's crucial to consider this diagnosis due to its potential severity and the fact that patients might not always recall or admit to such exposure. The presentation of lymphadenopathy, especially in the axilla, and systemic symptoms like nausea and vomiting, along with elevated liver enzymes, could be consistent with cat-scratch disease.
Lymphoma: Although less likely given the acute presentation following bites, lymphoma can cause lymphadenopathy and should be considered, especially if the lymph nodes do not resolve with treatment of the presumed cause.

Tick-borne illnesses (e.g., Lyme disease, Southern tick-associated rash illness): Depending on the geographic location, tick-borne illnesses could be a consideration, especially if the patient was in an area where ticks are common. These illnesses can cause lymphadenopathy, systemic symptoms, and elevated liver enzymes.
Spider bites with systemic manifestations (e.g., brown recluse spider bite): Certain spider bites can cause systemic symptoms, including nausea, vomiting, and elevated liver enzymes, in addition to local reactions and lymphadenopathy. However, such cases are rare and would depend on the specific spider species present in the patient's area.