The rapid deployment of sixth-generation (6G) wireless networks coupled with the Internet of Things (IoT) has revolutionized healthcare systems, enabling real-time medical data collection and processing through interconnected medical devices. However, the massive scale of medical data generated by these 6G-IoT healthcare networks raises critical concerns regarding data privacy, security, and trustworthiness. Traditional centralized medical data management systems suffer from single points of failure, privacy breaches, and unauthorized access to sensitive patient information. This paper proposes a novel blockchain-based dynamic sharding framework specifically designed for securing trustworthy medical data in 6G-IoT environments, termed TRUST-Med6G. Our approach employs a two-stage optimization strategy that combines reputation-based medical device authentication with deep reinforcement learning-driven adaptive sharding mechanisms. The first stage utilizes a delegated Byzantine fault tolerance protocol to establish trust among medical IoT devices based on their historical reliability and data authenticity records. The second stage implements a dueling deep Q-network algorithm to dynamically optimize blockchain sharding configurations dynamically, minimizing cross-shard medical data transactions while maximizing system throughput and privacy protection. Experimental evaluation against six baseline methods demonstrates that TRUST-Med6G achieves superior performance across all metrics, reducing cross-shard collaborative medical data transactions by over 50% while maintaining privacy protection effectiveness above 95% for highly sensitive medical information and demonstrating exceptional resilience against malicious devices in 6G-IoT healthcare environments.