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Low-latency storage in healthcare analytics has become critical as modern hospitals generate terabytes of multimodal data from electronic health records (EHRs), medical imaging, and real-time monitoring devices. Traditional storage architectures relying on static caching policies such as Least Recently Used (LRU) or Least Frequently Used (LFU) are inadequate to handle the dynamic and heterogeneous nature of healthcare workloads. These rule-based approaches often limited from high I/O latency, inefficient cache utilization, and performance degradation under concurrent access conditions. To address these limitations, this study introduces a hybrid Convolutional Neural Network (CNN)-Transformer framework for intelligent and adaptive low-latency storage optimization in AI-driven healthcare systems. The model leverages a CNN to extract localized access patterns from structured access logs and a Transformer to capture long-term temporal dependencies in data usage. These insights are used to predict access hotness scores, enabling proactive caching and prefetching across a multi-tier storage architecture that includes Dynamic Random-Access Memory (DRAM), Solid-State Drive (SSD), Hard Disk Drive (HDD), and cloud storage. Experiments conducted using the MIMIC-IV dataset demonstrate that the proposed framework achieves an average latency of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1. 9 4 m s}$</tex>, a cache hit ratio of 95.8%, throughput of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$317 \text{MB} / \mathrm{s}$</tex>, and prediction accuracy of 97.6%, maintaining robust performance even under high-load scenarios up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1 0 0 0 0}$</tex> simulated concurrent requests. These results demonstrate the framework's ability to dynamically anticipate data access trends, reduce redundant migrations, and ensure efficient resource utilization. This study paves the way for deploying intelligent, Artificial Intelligence (AI)-enabled storage infrastructures that deliver real-time responsiveness and scalability in hospital-wide analytics, remote patient monitoring, and critical care applications, thereby advancing the future of low-latency healthcare data management.