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Despite their promise, these models remain highly sensitive to subtle prompt perturbations, both lexical and syntactic, posing serious risks in safety-critical clinical applications. In this study, we conduct a systematic sensitivity analysis to evaluate the robustness of both general-purpose (e.g., GPT-3.5, Llama3) and medical-specific LLMs (e.g., ClinicalBERT, BioLlama3, BioBERT) using the MedMCQA benchmark. We categorize perturbations into natural and adversarial types and examine their effect on model consistency, accuracy, and reliability in clinical reasoning tasks. Our findings reveal that medical LLMs are not intrinsically safe. Even minor variations in phrasing can alter clinical advice, and targeted adversarial prompts can provoke harmful outputs. 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