The exponential proliferation of healthcare data from wearable devices, medical sensors, and electronic health records demands advanced analytical approaches for early disease detection and prediction. As IoT devices become increasingly prevalent, they generate substantial volumes of data, which can enhance clinical decision-making and optimize resource management when analyzed proficiently. This influx of big data has intensified the efforts of healthcare scientists to manage and analyze such an enormous volume of data, potentially disrupting the inference process at decision centers. Handling and analyzing data from these devices has become extraordinarily challenging, presenting numerous obstacles for the research community. Furthermore, integrating data analytics and IoT to enable real-time, context-aware data analytics remains a significant hurdle. Traditional analysis techniques, such as linear regression, are woefully inadequate in coping with the explosive growth of health big data. To address these challenges, we proposed a novel architecture for big data analytics and processing in Healthcare Internet of Things (H-IoT) applications focused on multi-disease prognosis by integrating edge computing with cloud-based analytics to enable real-time health data processing while addressing privacy concerns. The proposed system balances computational requirements with the need for real-time processing and privacy preservation through a four-layer architecture: Data Acquisition, Edge Processing, Cloud Analytics, and Application. Our proposed framework incorporates machine learning algorithms optimized for healthcare data heterogeneity and demonstrates superior performance in predicting multiple chronic conditions, including cardiovascular diseases, diabetes complications, and respiratory disorders. Experimental evaluation demonstrates the system's efficacy in predicting multiple chronic conditions. Results show a 27% improvement in prediction accuracy and a 43% reduction in latency compared to traditional cloud-only solutions. This work contributes to advancing predictive healthcare analytics by providing a scalable, privacy-preserving, and computationally efficient system for multi-disease prognosis in IoT-enabled healthcare environments, with distributed computing paradigms to enable efficient processing of heterogeneous health data streams while maintaining HIPAA compliance. The proposed system establishes a robust foundation for developing next-generation clinical decision support systems that capitalize on the extensive data streams produced by healthcare IoT (H-IoT) technologies.