The Internet of Healthcare Things (IoHT) is rapidly evolving, providing new opportunities to enhance healthcare delivery. However, the resource limitation of connected medical sensing devices leads to congestion, resulting in reduced network performance, delayed data transmission, and loss of critical medical information, which can have significant consequences in healthcare. To address this issue, this paper proposes an Enhanced Hybrid Congestion Mitigation Strategy (EHCMS) for IPv6 over low-power wireless personal area networks (6LoWPAN) and routing protocol for low-Power and lossy networks (RPL) based patient-centric IoHT (PC-IoHT). The EHCMS combines several techniques, including traffic management, network topology optimization, and load balancing, to enhance network performance and reduce congestion. The proposed framework is a hybrid strategy that utilizes resource- and traffic-control mechanisms to alleviate congestion in the 6LoWPAN-RPL-based patient-centric IoHT network. For the resource-control-based approach, a congestion-aware composite objective function is designed using a few congestion-specific routing metrics and formulated as a multi-attribute decision-making problem solved using Grey relational analysis (GRA). In addition, a non-linear multi-criteria optimization problem-based transmission rate adaptation mechanism is contrived as a traffic-control scheme for congestion mitigation. The effectiveness of the proposed EHCMS is evaluated using simulations on the Cooja simulator in the Contiki-3.0 OS and compared with existing congestion-alleviating strategies. The results demonstrate that the proposed framework can significantly reduce congestion in the IoHT network, perform better than existing works, and improve the quality of service. This research paper contributes to the field of IoHT by proposing an effective congestion mitigation strategy that enhances the reliability and performance of the PC-IoHT network, ultimately improving the quality of healthcare delivery.