A significant evolution in healthcare recently uses technological advancements to perform different activities, such as patient electronic medical records (EMRs) data gathering, preserving, processing, diagnosis, and handling. The adaptation of the Internet of Things (IoT) and cloud has further facilitated the enhancement of related healthcare systems, which can considerably improve data connectivity, accessibility, and exchange, which leads to a significant improvement in the quality of services to patients. Furthermore, scientific computations over data in transmission can be exposed to adversaries and may reveal private data for financial benefit. This article uses the Cheon-Kim-Kim-Song fully homomorphic encryption scheme and IOTA Tangle using masked authenticated messaging (MAM) protocol to provide secure communication between patient and doctor. CKKS-FHE-based data encryption provides data privacy, and secured EMRs sharing through IOTA Tangle guarantees data confidentiality. The performance of this work is analyzed in terms of encryption and decryption time, and payload sharing using MAM and NON-MAM protocols results in evidence of the effectiveness of the approach and improves overall security. The proposed scheme performs better overall computation time and performance than other relevant schemes. Further, the security analysis shows that the proposed system is resilient to data immutability and integrity, forward secrecy, and passive and active attacks.