Muscle Strain: The patient's symptoms of lower neck pain with neck extension, in the context of a recent upper respiratory infection (URI), are most consistent with a muscle strain. This is a common condition that can occur due to coughing fits associated with URIs, which can strain the muscles in the neck.

Cervical Lymphadenitis: This condition, characterized by inflammation of the lymph nodes in the neck, can be a complication of a URI. The presence of neck pain, especially if it's localized and tender, could suggest lymphadenitis.
Acute Bronchitis: While primarily a respiratory condition, acute bronchitis can cause significant coughing, which might lead to neck pain due to the strain on neck muscles.

Epidural Abscess or Meningitis: Although less likely, these conditions are medical emergencies that require prompt diagnosis and treatment. Neck pain, especially with fever (even though the patient does not have a fever currently), and stiffness could be indicative of these serious conditions.
Tuberculosis (TB): TB can cause neck pain and lymphadenopathy. Although less common in young, otherwise healthy individuals, it's a critical diagnosis not to miss due to its public health implications and the need for specific treatment.
Lymphoma: This is another serious condition that could present with lymphadenopathy and neck pain. It's less likely in the context of a recent URI but is crucial not to miss.

Retropharyngeal Abscess: A rare but serious condition that can cause neck pain and stiffness, often accompanied by difficulty swallowing and fever. It's more common in children but can occur in adults.
Osteomyelitis of the Cervical Spine: An infection of the cervical spine bones, which could present with neck pain and stiffness. This condition is rare and usually occurs in the context of bacteremia or direct infection.
Spinal Epidural Hematoma: A rare condition that can cause sudden onset of neck pain and neurological deficits. It's often associated with trauma or anticoagulation but can occur spontaneously.