Sarcoidosis: This condition is characterized by the formation of granulomas in various organs, including the lungs and lymph nodes. The patient's symptoms of anorexia, arthralgias, cough, and the radiographic findings of air trapping and hilar lymphadenopathy are consistent with pulmonary sarcoidosis. Lab findings likely to support this diagnosis include elevated angiotensin-converting enzyme (ACE) levels, although this is not specific, and a positive gallium scan.

Lymphoma: Both Hodgkin's and non-Hodgkin's lymphoma can present with systemic symptoms such as anorexia and arthralgias, along with cough and hilar lymphadenopathy if the disease involves the chest. Lab findings might include abnormal lymphocyte counts and specific markers depending on the lymphoma type.
Tuberculosis (TB): Although less common in some regions, TB can cause a wide range of symptoms including cough, anorexia, and arthralgias. Hilar lymphadenopathy and air trapping can be seen on chest X-ray. Lab findings would include a positive purified protein derivative (PPD) test or interferon-gamma release assay, and potentially positive sputum or tissue cultures for Mycobacterium tuberculosis.
Histoplasmosis: This fungal infection can mimic sarcoidosis and TB, causing similar symptoms and radiographic findings. Lab diagnosis is typically made through antigen detection, serology, or culture.

Lung Cancer: Although less likely given the two-month history and the specific combination of symptoms, lung cancer can cause cough, anorexia, and if advanced, systemic symptoms like arthralgias. Hilar lymphadenopathy can be present if the cancer has spread to lymph nodes. Lab findings would depend on the type of cancer but might include abnormal tumor markers.
Wegener's Granulomatosis (Granulomatosis with Polyangiitis, GPA): This is a form of vasculitis that can affect the lungs and kidneys, presenting with a variety of symptoms including cough, arthralgias, and systemic symptoms. Lab findings might include positive c-ANCA (cytoplasmic antineutrophil cytoplasmic antibodies) and elevated inflammatory markers.

Langerhans Cell Histiocytosis (LCH): This rare disorder can cause pulmonary symptoms, including cough and radiographic abnormalities like air trapping and nodules. Systemic symptoms can also occur. Diagnosis is typically made through biopsy.
Erdheim-Chester Disease: A rare form of histiocytosis that can involve the lungs, among other organs, and present with systemic symptoms and radiographic findings similar to those described. Diagnosis is made through biopsy and genetic testing.