A 52-year-old woman with a history of acute myocardial infarction 2 days ago now presents with persistent hypotension (BP 88/56 mmHg), elevated jugular venous pressure (JVP 8 cm H₂O), clear lung fields, and reduced urine output (0.3 mL/kg/hr). Electrocardiography shows inferior wall MI. Which investigation is most appropriate to differentiate between cardiogenic shock due to right ventricular infarction versus acute mechanical complication in this patient?