Rheumatic Fever: This condition is characterized by fever, joint pain (which could include finger pain), and a rash, following a streptococcal infection. The elevated ESR (erythrocyte sedimentation rate) supports an inflammatory process. Atypical pneumonia could be a preceding infection triggering the autoimmune response.

Lupus (Systemic Lupus Erythematosus): Lupus can present with a wide range of symptoms including joint pain, diffuse rash, and systemic inflammation (elevated ESR). It can also involve the lungs, causing pneumonia. The combination of symptoms makes lupus a plausible diagnosis.
Rheumatoid Arthritis (RA): While RA primarily causes joint pain and inflammation, it can also be associated with systemic symptoms like fever and rash. Interstitial lung disease, a complication of RA, could present as atypical pneumonia. Elevated ESR is common in active RA.
Psoriatic Arthritis: This condition combines the swollen, scaly skin of psoriasis with joint pain and arthritis. It could explain the rash and finger pain, and while less common, psoriatic arthritis can be associated with lung involvement and elevated inflammatory markers.

Endocarditis: Although less likely, infective endocarditis can present with systemic symptoms including fever, rash (e.g., Janeway lesions), and joint pain due to septic emboli. The elevated ESR would support an infectious or inflammatory process. Atypical pneumonia could be a source of the infection.
Lymphoma: Certain types of lymphoma, particularly those involving the skin (like cutaneous T-cell lymphoma), can cause a diffuse rash. Systemic symptoms such as fever and weight loss are common, and lymphoma can involve the lungs, causing atypical pneumonia. An elevated ESR is a nonspecific marker of inflammation that could be seen in lymphoma.

Relapsing Polychondritis: This rare autoimmune disorder involves cartilage and can cause a variety of symptoms including joint pain, rash, and respiratory issues due to cartilage involvement in the trachea and lungs. It's a less common condition but could fit the broad range of symptoms described.
Sarcoidosis: While more commonly associated with lung and lymph node involvement, sarcoidosis can cause skin rashes, joint pain, and elevated ESR. It's a diagnosis of exclusion but should be considered in patients with multi-system involvement and atypical presentations.