This study aims to enhance energy efficiency and network throughput in Narrowband IoT (NB-IoT) and Narrowband Cognitive Radio IoT (NB-CR-IoT) networks. A novel three-hop communication strategy is proposed, employing a double auction mechanism to optimize relay selection and extend the battery life of cell-edge NB-IoT users (CENUs). The approach is supported by the EENU-MWM algorithm, which ensures efficient and fair user matching. With the rapid proliferation of IoT devices, critical challenges such as spectrum congestion and hardware limitations for continuous sensing have emerged. To address these issues, the study introduces optimized sensing parameters and relay node selection strategies within NB-CR-IoT and Narrowband Cognitive Radio Internet of Medical Things (NB-CR-IoMT) frameworks. These enhancements improve overall data throughput while reducing transmission power consumption.