This paper presents a novel architecture integrating edge computing, deep learning, and blockchain to enable secure and real-time medical diagnostics. The system collects physiological signals, such as Electrocardiogram (ECG) data, from wearable medical electronics and processes them locally using a lightweight convolutional neural network (CNN) optimized for edge deployment. To ensure data integrity and auditability, the inference results are securely logged on a permissioned blockchain using smart contracts. The proposed framework eliminates reliance on cloud infrastructure, supports decentralized trust, and preserves patient privacy. Using the MIT-BIH Arrhythmia dataset, we evaluated the system on Raspberry Pi 4, Jetson Nano, and Coral Dev Board. The CNN model achieved over 92% accuracy with inference times as low as 9 ms, and blockchain commit latency remained under 500 ms. Our results demonstrate that this pipeline is well-suited for resource-constrained or privacy-sensitive healthcare environments, offering a practical solution for trusted, on-device medical AI.