Edge computing (EC) and the Internet of Things (IoT) have transformed healthcare, especially real-time patient monitoring. This comprehensive study explores the architecture, implementation, and clinical impacts of edge computing in the healthcare sector. It assesses workloads, network conditions, and the capabilities of devices for real-time processing. This paper proposes a Healthcare Metropolitan Area Network (HMAN) architecture to support health-related applications and services across the city. Unlike existing models, we propose a Data Flow Offloading (DFO) algorithm that introduces a multi-layer hierarchical structure for handling high volumes of patient data. It ensures scalability by utilizing distributed clouds in extreme overload situations like pandemics. The proposed approach attains a faster system response time than existing models.