As an important carrier of healthcare data, Electronic Medical Records (EMRs) generated from various sensors, i.e., wearable, implantable, are extremely valuable research materials for artificial intelligence and machine learning. The efficient circulation of EMRs can improve remote medical services and promote the development of the related healthcare industry. However, in traditional centralized data sharing architectures, the balance between privacy and traceability still cannot be well handled. To address the issue that malicious users cannot be locked in the fully anonymous sharing schemes, we propose a trackable anonymous remote healthcare data storing and sharing scheme over decentralized consortium blockchain. Through an "on-chain & off-chain" model, it relieves the massive data storage pressure of medical blockchain. By introducing an improved proxy re-encryption mechanism, the proposed scheme realizes the fine-gained access control of the outsourced data, and can also prevent the collusion between semi-trusted cloud servers and data requestors who try to reveal EMRs without authorization. Compared with the existing schemes, our solution can provide a lower computational overhead in repeated EMRs sharing, resulting in a more efficient overall performance.