Interactive medical diagnosis requires an agent to gather patient evidence through sequential questions before committing to a diagnosis. Large language models (LLMs) now make such consultations feasible, and existing approaches typically select questions by how much they reduce uncertainty among candidate diseases. However, this objective is insensitive to the unequal clinical costs of diagnostic errors and omitted severe alternatives, so minimizing uncertainty need not minimize final diagnostic loss. To bridge this gap, we propose CaRDI (Calibrated Risk for Diagnostic Interaction), a planning framework built around a clinical loss combining primary diagnosis error with severity-weighted differential omission. Diagnostic and safety beliefs estimate the two loss components, while conformal residual calibration corrects for underestimation from partial evidence. The calibrated risk then guides question selection and stopping by balancing expected risk reduction against interaction cost. Experiments on multiple medical benchmarks show that CaRDI improves accuracy while requiring fewer questions. Further analysis shows that replacing entropy with clinical risk as the planning objective reduces clinical loss by 21.5% and decreases severe omissions. Our code is available at https://anonymous.4open.science/r/CaRDI-A940/.

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