Answer: Pulled elbow.
Step 1: The history is a sudden axial pull or swing on an extended, pronated arm in a young child. This is the classic mechanism of pulled elbow (nursemaid's elbow), a subluxation of the radial head out of the annular ligament.
Step 2: The child holds the affected arm still, often slightly flexed and pronated or held by the side, refuses to use it, and resents being touched, but there is no significant swelling or deformity.
Step 3: A supracondylar fracture or elbow dislocation would usually follow a fall on an outstretched hand and show marked swelling or deformity. A radial head fracture is uncommon at this age and again usually follows a fall, not a simple pull.
Step 4: The pull mechanism with no deformity is typical of pulled elbow. A fracture should still be excluded, but the clinical picture is diagnostic. Ref: Apley and Solomon's System of Orthopaedics.