Cellulitis with possible abscess formation: The patient's symptoms of worsening elbow swelling, warmth, and spreading to the hand, along with elevated CRP and WBC, are highly suggestive of a bacterial infection such as cellulitis. The age of the patient and the severity of the inflammatory markers support this diagnosis.

Septic arthritis: Although less likely than cellulitis due to the lack of specific joint pain or history of trauma, septic arthritis is a consideration, especially given the proximity of the swelling to the elbow joint and the systemic signs of infection.
Deep vein thrombosis (DVT): The swelling and warmth could also suggest a DVT, particularly in an elderly patient who may be at higher risk for thrombotic events. However, the presence of significant systemic inflammation (high CRP and WBC) makes this less likely as the primary diagnosis.
Osteomyelitis: Infection of the bone could present with swelling, warmth, and elevated inflammatory markers. However, it typically requires a longer duration of symptoms and may be associated with more localized pain and possibly a history of trauma or recent surgery.

Necrotizing fasciitis: Although rare, this condition is life-threatening and requires immediate surgical intervention. The presence of severe pain out of proportion to the physical findings, rapid progression of symptoms, and signs of systemic toxicity should raise suspicion for necrotizing fasciitis.
Endocarditis with septic emboli: In an elderly patient with a new heart murmur or known valvular disease, endocarditis with septic emboli to the arm could present with swelling, warmth, and systemic signs of infection. This diagnosis is critical to consider due to its high mortality rate if untreated.

Rheumatologic conditions (e.g., rheumatoid arthritis flare, lupus): While these conditions can cause significant joint inflammation and systemic symptoms, the acute onset and severity of the patient's presentation, along with the lack of prior diagnosis or suggestive history, make them less likely.
Malignancy (e.g., lymphoma, leukemia): Certain malignancies can cause localized swelling and systemic inflammation, but they would be unusual as the primary presentation in this scenario without other supporting evidence such as lymphadenopathy, weight loss, or abnormal blood cell counts suggestive of malignancy.