With more devices being inter- or intra-connected, Internet of Things (IoT) has gradually been adopted in many disciplines, such as healthcare industry, coined as Internet of Medical Things (IoMT). The purpose of IoMT is to facilitate the efficiency and effectiveness of medical operations, i.e., remotely monitoring the status of patients. In such healthcare environments, smartphones have become an important device to communicate with others and update the information of patients, resulting in a special type of IoMT called Medical Smartphone Networks (MSNs). To reinforce the distributed architecture, trust management schemes are often implemented to defend against insider attacks. However, how to maintain the robustness of trust management in heavy traffic networks still remains a challenge, i.e., COVID-19 incident would cause excessive traffic for healthcare organizations and increase the difficulty of validating trustworthiness among MSN nodes. In this work, we focus on this issue and propose a blockchain-enabled adaptive traffic sampling method to help enhance the robustness of trust management under high traffic environments. The use of blockchain technology aims to build a verified database of malicious traffic among all nodes. The evaluation in a real healthcare environment demonstrates the viability and effectiveness of our approach.