Choosing messaging protocols for Internet-of-Medical-Things (IoMT) deployments demands balancing latency, reliability, energy, security, and interoperability under clinical risk. We present a clinically risk-aware decision framework that models uncertainty using circular q-rung orthopair fuzzy information and combines Muirhead-mean fusion with TOPSIS ranking. Each protocol–criterion assessment captures supporting evidence, counterevidence, and confidence derived from empirical variability. Safety-critical criteria (e.g., alarm latency, packet loss, cybersecurity posture) are handled with an asymmetric scoring scheme that penalizes risk more strongly than it rewards gains, reflecting bedside priorities. Evidence from multiple scenarios and assessors is fused through a risk-weighted Muirhead-mean to preserve interactions across settings such as home monitoring, ambulatory care, and ICU. Clinical hard constraints (for example, mandated encryption or maximum alarm delay) are enforced via a feasibility screen prior to ranking, ensuring only deployable options are compared. The final ordering is obtained with TOPSIS, and robustness is quantified through sensitivity analyses over modeling choices and weights. Results on representative IoMT protocols (MQTT, MQTT-SN, CoAP, HTTP(S)…) show that clinically risk-aware modeling can change the preferred protocol relative to symmetric scoring, making trade-offs between speed, energy, and safety explicit for decision. We evaluate 12 standardized protocols against 10 criteria across home, ambulatory, and ICU scenarios.