Flexible sharing of electronic medical records (EMRs) is an urgent need in healthcare, as fragmented storage creates EMR management complexity for both practitioners and patients. Blockchain has emerged as a promising solution to address the limitations of centralized EMR systems regarding interoperability, data ownership, and trust concerns. Whilst its healthcare implementation continues to face scalability challenges, particularly in uploading lag time as EMR volumes increase. In this paper, we describe the design of a novel blockchain-based data structure, MedBlockTree, which aims to solve the scalability issue in blockchain-based EMR systems, particularly low block throughput and patient awareness. MedBlockTree leverages a chameleon hash function to generate collision blocks for existing patients and expand a single chain into a growing block tree with $n$ branches that are capable of processing $n$ new blocks in a single consensus round. We also introduce the EnhancedPro consensus algorithm to manage multiple branches and maintain network consistency. Our comprehensive simulation evaluates performance across four dimensions: branch number, worker number, collision rate, and network latency. Comparative analysis against a traditional blockchain-based EMR system demonstrates outstanding throughput improvements across all dimensions, achieving processing speeds $ν\cdot n$ times faster than conventional approaches.