<p>The convergence of IoT and healthcare has enabled real-time, remote patient monitoring and improved medical service delivery. Security and privacy in these emerging technologies are paramount due to the sensitive nature of the data and the vulnerabilities inherent in IoT infrastructures. Conventional cryptographic solutions, widely used to secure healthcare data, are increasingly threatened by the advent of quantum computing, which is expected to compromise existing algorithms. To address these concerns, this paper proposes a novel quantum-enabled end-to-end security protocol tailored for IoT-based remote healthcare monitoring systems. The proposed framework leverages both Semi-Quantum Key Distribution (SQKD) and Mediated Semi-Quantum Key Distribution (MSQKD) to facilitate secure communication between heterogeneous devices with limited quantum capabilities, through the assistance of fully quantum Multi-access Edge Computing (MEC). Our protocol addresses key challenges in applying quantum-enabled solution to healthcare environments by (i) allowing semi-quantum devices to participate in secure key exchange with support from fully quantum-capable edge nodes, (ii) eliminating the need for pre-established trusted authenticated channels, and (iii) supporting emergency scenarios, where MSQKD ensures fast, direct, and secure communication between patient devices and healthcare centers. Security and performance analysis demonstrate improved efficiency and protocol resistance against a wide range of quantum-based threats.</p>