The most likely diagnosis is reactive arthritis (formerly known as Reiter syndrome), a noninfectious inflammatory arthritis that can occur approximately 3 to 6 weeks after a gastrointestinal or genitourinary infection. It is common for infection to have resolved and stool culture to become negative by the time arthritis begins. Asymmetric monoarthritis or oligoarthritis in the lower extremities is the most common presentation, but up to 20% of patients have polyarthritis. Enthesopathy (inflammation at the site where ligaments, tendons, joint capsule or fascia attaches to bone), dactylitis, and sacroiliitis may occur. Erosive disease is uncommon. Ophthalmologic inflammation is a feature of this disease in up to 30% of patients and can manifest as uveitis or conjunctivitis. This patient's manifestations, including a diarrheal illness that preceded the onset of arthritis by 2 to 3 weeks, inflammatory oligoarticular involvement of lower extremities, inflammation of the insertion of the Achilles tendon, and anterior uveitis, are typical of reactive arthritis.

In bacterial infections, synovial fluid analysis typically reveals a neutrophilic leukocytosis (typically >50,000/µL [50 × 10⁹/L]), but synovial fluid leukocyte counts ≤50,000/µL (50 × 10⁹/L) do not definitively rule out infection. In this patient, infectious arthritis is less likely because this patient has no fever or leukocytosis on complete blood count.

Although psoriatic arthritis can present as an oligoarthritis, it is also less likely because the patient has no evidence of psoriasis on physical examination.

Rheumatoid arthritis is unlikely because it usually is a symmetric small joint polyarthritis rather than large joint oligoarthritis, and enthesopathy is not common.