Large language models (LLMs) exhibit remarkable capabilities in visual inspection of medical time-series data, achieving proficiency comparable to human clinicians. However, their broad scope limits domain-specific precision, and proprietary weights hinder fine-tuning for specialized datasets. In contrast, small specialized models (SSMs) excel in targeted tasks but lack the contextual reasoning required for complex clinical decision-making. To address these challenges, we propose ConMIL (Conformalized Multiple Instance Learning), a decision-support SSM that integrates seamlessly with LLMs. By using Multiple Instance Learning (MIL) to identify clinically significant signal segments and conformal prediction for calibrated set-valued outputs, ConMIL enhances LLMs' interpretative capabilities for medical time-series analysis. Experimental results demonstrate that ConMIL significantly improves the performance of state-of-the-art LLMs, such as ChatGPT4.0 and Qwen2-VL-7B. Specifically, \ConMIL{}-supported Qwen2-VL-7B achieves 94.92% and 96.82% precision for confident samples in arrhythmia detection and sleep staging, compared to standalone LLM accuracy of 46.13% and 13.16%. These findings highlight the potential of ConMIL to bridge task-specific precision and broader contextual reasoning, enabling more reliable and interpretable AI-driven clinical decision support.