Internet of Medical Things (IoMT) is becoming ubiquitous with a proliferation of smart medical devices and applications used in smart hospitals, smart-home based care, and nursing homes. It utilizes smart medical devices and cloud computing services along with core Internet of Things (IoT) technologies to sense patients' vital body parameters, monitor health conditions and generate multivariate data to support just-in-time health services. Mostly, this large amount of data is analyzed in centralized servers. Anomaly Detection (AD) in a centralized healthcare ecosystem is often plagued by significant delays in response time with high performance overhead. Moreover, there are inherent privacy issues associated with sending patients' personal health data to a centralized server, which may also introduce several security threats to the AD model, such as possibility of data poisoning. To overcome these issues with centralized AD models, here we propose a Federated Learning (FL) based AD model which utilizes edge cloudlets to run AD models locally without sharing patients' data. Since existing FL approaches perform aggregation on a single server which restricts the scope of FL, in this paper, we introduce a hierarchical FL that allows aggregation at different levels enabling multi-party collaboration. We introduce a novel disease-based grouping mechanism where different AD models are grouped based on specific types of diseases. Furthermore, we develop a new Federated Time Distributed (FedTimeDis) Long Short-Term Memory (LSTM) approach to train the AD model. We present a Remote Patient Monitoring (RPM) use case to demonstrate our model, and illustrate a proof-of-concept implementation using Digital Twin (DT) and edge cloudlets.