Efficient optimization of computational resources in Mobile Edge Computing (MEC)-enabled Internet of Things (IoT) environments is critical for enhancing energy efficiency and minimizing latency. This research focuses on medical image analysis, specifically kidney tumor segmentation using CT scan images from the KiTS19 dataset. To address the challenges of high computational demands and complex feature extraction, we propose an integrated framework that combines two advanced technologies: quantum-inspired operations implemented through classical simulation along with a Residual U-Net architecture for improved computation and post-quantum cryptography for robust security. The quantum-inspired neural network design leverages principles from quantum computing to create classical algorithms that boost computational efficiency, enabling faster and more accurate segmentation of medical images within resource-constrained IoT environments. Additionally, the framework employs a quantum-inspired Double Deep Reinforcement Learning (QiDDRL) strategy to dynamically optimize resource allocation, further enhancing segmentation accuracy while reducing latency. To safeguard data transmission between IoT devices and MEC servers, the system incorporates post-quantum cryptographic techniques-specifically Kyber for encryption and Dilithium for digital signatures-providing resistance against potential quantum-computing attacks. The proposed approach achieves 98 % segmentation accuracy on the KiTS19 dataset while addressing deep learning challenges such as the vanishing gradient problem, resulting in stable model performance. Overall, this combination of quantum-inspired computing and reinforcement learning with post-quantum cryptographic protection demonstrates the potential for secure and efficient medical image analysis in IoT environments, contributing to improved diagnostics and treatment planning in resource- and security-constrained healthcare settings.