Step 1: Identify the clinical pattern. There is regional pain disproportionate to the original injury (a sprain), persisting and worsening after the injury should have healed, with autonomic and trophic changes (edema, shiny skin) localized to the affected limb.
Step 2: Recognize the syndrome. This constellation of disproportionate regional pain plus vasomotor, sudomotor and trophic skin changes after a noxious event defines complex regional pain syndrome (CRPS).
Step 3: Distinguish CRPS type 1 from type 2. CRPS type 1 (formerly reflex sympathetic dystrophy) follows trauma WITHOUT a definable nerve injury. CRPS type 2 (formerly causalgia) follows a documented peripheral nerve injury.
Step 4: Apply to this case. A simple ankle sprain is a soft tissue injury with no identifiable major nerve lesion, so this is CRPS type 1.
Step 5: Exclude other options. Fibromyalgia is widespread, not regional or trophic. Peripheral neuropathy gives a stocking-glove sensory pattern, not localized shiny edematous skin after a sprain.
Conclusion: The correct answer is option B, complex regional pain syndrome type 1.