Traditional healthcare systems frequently become overcrowded and unable to provide timely treatment due to the continual rise in patient numbers caused by the rapid global population growth. Digital technology integration, and the Internet of Things (IoT) in particular, has the ability to revolutionise healthcare by offering up the opportunity to the establishment of smart healthcare systems. Patients, no matter where they live, will have better access to healthcare systems, which allow for remote monitoring, real-time tracking, and less reliance on in-person hospital visits. But there are a lot of challenges to overcome when putting these systems into action. For example, there are concerns about the security of sensitive medical data, vulnerabilities in inexpensive smart devices, and centralized IoT designs that are prone to single points of failure. Furthermore, high data processing demands are also introduced by the exponential rise of IoT devices. To address these issues, we proposed a unique Blockchain-Edge-IoT framework called Smart Scalable Medical Infrastructure (SSMI) for the establishment of smart healthcare systems. To reduce the load on cloud servers and data processing times, SSMI uses edge computing to handle patient data close to its source, making it scalable, secure, immutable, and decentralised. Smart contracts are included in the architecture to facilitate the enforcement of privacy policies and the establishment of conditional access for untrusted parties. Additionally, researchers have implemented a Device Monitor to regulate and track inexpensive and vulnerable smart gadgets. The experimental results illustrate that the proposed framework is more efficient in terms of processing latency, data throughput, and security resilience than the existing healthcare models.