Septic Arthritis: Given the acute onset of knee pain, swelling, redness, and the patient's history of chills, septic arthritis is a strong consideration. The patient's inability to bend the knee due to pain and the absence of trauma also support this diagnosis. The presence of chills suggests a possible infectious etiology.

Gouty Arthritis: Although the patient mentions that gout typically does not affect his knee, it is still a possibility, especially given his history of gout. The acute onset of pain, swelling, and redness could be consistent with a gout flare.
Pseudogout (Calcium Pyrophosphate Deposition Disease, CPPD): Similar to gout, pseudogout can cause acute, inflammatory arthritis, particularly in the knee, and could be considered given the patient's age and presentation.
Traumatic Hemarthrosis: Despite the patient's denial of trauma, it's possible that a minor, unnoticed injury could have led to bleeding into the joint, causing pain and swelling.

Osteomyelitis: Although less common, osteomyelitis (bone infection) could present with similar symptoms and is crucial to diagnose early due to its potential for serious complications.
Neoplastic Processes: Tumors, either primary or metastatic, could cause knee pain and swelling, especially in an older adult. Given the patient's age and the acute presentation, it's essential to consider this, although it might be less likely.
Deep Vein Thrombosis (DVT): While the presentation is not typical for DVT, the patient's age and the presence of swelling and pain could potentially mask a DVT, which is a medical emergency.

Rheumatoid Arthritis Flare: Although the patient does not mention a history of rheumatoid arthritis, a flare could potentially present with acute knee symptoms. However, the lack of systemic symptoms or a known history makes this less likely.
Lyme Arthritis: If the patient has been exposed to ticks, Lyme disease could be a consideration, especially if the presentation includes a distinctive "bull's-eye" rash, which is not mentioned here.
Hemophilic Arthropathy: In patients with a history of hemophilia, recurrent joint bleeds can lead to chronic arthritis. However, this would be highly unusual without a known history of hemophilia.

Complete Blood Count (CBC): To look for signs of infection or inflammation.
Erythrocyte Sedimentation Rate (ESR) and C-Reactive Protein (CRP): To assess for systemic inflammation.
Blood Cultures: If septic arthritis is suspected, to identify the causative organism.
Synovial Fluid Analysis: Crucial for diagnosing septic arthritis, gout, and pseudogout. The fluid should be sent for cell count, crystal examination, and culture.
Imaging: X-rays to rule out fractures or osteomyelitis, and possibly an ultrasound or MRI if concerned about DVT or soft tissue abnormalities.
Urinalysis: To rule out urinary tract infection as a source of sepsis or to evaluate for kidney stones, which could cause referred pain.
Consider Lyme Titer: If exposure history is positive or if the patient is from an endemic area.