In a typical Internet of Medical Things (IoMT) system, it is common for users’ physiological data, collected by medical sensors, to be processed and shared in a third-party environment, such as a cloud server. Medical data sharing in a third-party environment must guarantee data integrity and source authentication, and robust privacy-preserving measures must be taken to enhance reliability. Searchable encryption (SE) has been leveraged in the IoMT to address the issue of exposing private data during storage and transmission. However, existing works suffer from shortcomings, such as vulnerability to data tampering. In this paper, we propose a novel privacy-preserving data sharing scheme with identity authentication based on SE that addresses the heavyweight public key management problem within a Public Key Infrastructure (PKI) framework. In IB-BPSE, a redactable signature (RS) assisted by blockchain and Merkle tree structure ensures authentication and integrity. Searchable proxy re-encryption encrypts private data, enabling efficient ciphertext search and multi-user data sharing. In addition, the scheme is provably secure in the random oracle model, and the performance analysis demonstrates that the system achieves ideal comprehensive performance. Finally, we propose an application scenario in IoMT based on IB-BPSE.