In cloud-assisted electronic health (eHealth) systems, the exponential growth of electronic health records (EHRs) has prompted healthcare organizations to move it to the cloud. However, EHRs are encrypted before being outsourced for privacy. Although searchable encryption schemes for EHRs have been proposed, their search efficiency and functionality for massive EHRs with high-dimensional are still insufficient. In this paper, we adopt an attribute hierarchy structure for medical datasets, enabling efficient multi-dimensional range search and reducing high-dimensional EHRs to low-dimensional vectors. To further improve search efficiency, we design an index tree that require no additional storage and computational overhead, significantly improving efficiency in search, trapdoor generation, and index building. Our scheme is well-suited for large-scale medical data scenarios, especially in dealing with high-dimensional and massive datasets. Extensive experiments demonstrate the superiority of our scheme over existing solutions, particularly in large-scale medical data scenarios. Compared to the classic EDMRS scheme, our scheme has a computational overhead in index building and search that is only about 1/500 and 1/10 of EDMRS when the number of keywords and electronic health records is 3,000 and 6,000, respectively. Moreover, as medical data and keywords increase, our scheme shows slower computational overhead growth compared to EDMRS.