Internet of Medical Things (IoMT) combines Internet of Things (IoT) with medical devices to facilitate healthcare, providing affordable solutions, and faster treatments to patients. An increase in IoMT use has led to several security/privacy challenges, since many IoMT devices have not been designed with security and privacy features in mind, which makes them vulnerable to attacks. Furthermore, as security risks and threats affect all the layers developed for IoMT-based architectures, an IoMT network must follow stricter privacy and security specifications compared to other IoT devices. In order to address this, we present a new IoT-based architecture to improve the data privacy, security, and integrity leveraging distributed InterPlanetary File System (IPFS) storage and blockchain. The data captured from medical devices is split into multiple encrypted pieces using Secret Sharing Algorithm (SSA) and these pieces are then stored in distributed IPFS storage hosted on edge and cloud servers, and their copies are verifiable by a blockchain network. The applied SSA method ensures that even if a piece of data is compromised, the original data is neither leaked nor lost. Our proposed architecture is implemented and tested on an IoMT-based monitoring system to investigate its feasibility, scalability, and performance.