Internet of Medical Things (IoMT) provides an excellent opportunity to investigate better automatic medical decision support tools with the effective integration of various medical equipment and associated data. This study explores two such medical decision-making tasks, namely COVID-19 detection and lung area segmentation detection, using chest radiography images. We also explore different cutting-edge machine learning techniques, such as federated learning, semi-supervised learning, transfer learning, and multi-task learning to explore the issue. To analyze the applicability of computationally less capable edge devices in the IoMT system, we report the results using Raspberry Pi devices as accuracy, precision, recall, Fscore for COVID-19 detection, and average dice score for lung segmentation detection tasks. We also publish the results obtained through server-centric simulation for comparison. The results show that Raspberry Pi-centric devices provide better performance in lung segmentation detection, and server-centric experiments provide better results in COVID-19 detection. We also discuss the IoMT application-centric settings, utilizing medical data and decision support systems, and posit that such a system could benefit all the stakeholders in the IoMT domain.