The continuous development of cloud computing and the Internet of Things accelerates the development of the revolutionary Internet of Medical Things. The seamless integration of cloud platforms into the Internet of Medical Things framework has structured the healthcare data management, processing, and real-time analytics. Cloud services provide a scalable, secure, and cost-effective infrastructure for storing, processing, and analyzing the vast volumes of data generated by Internet of Medical Things devices. However, this integration also introduces privacy and security concerns, as data becomes increasingly intertwined with cloud-based system integration. This systematic review meticulously examines the challenges and enhancements of privacy and security in a cloud-integrated Internet of Medical Things system. It identifies and analyzes, through four research questions, a wide spectrum of potential threats like unauthorized access to sensitive data, data breaches, device manipulation, and privacy violations and provides some enhancements on existing systems to tackle those issues efficiently.