The rapid expansion of the Healthcare Internet-of-Things (HIoT) has created new opportunities for delivering personalized, real-time medical intelligence. In such systems, IoT devices acquire data at the point of care, edge servers provide low-latency preprocessing and lightweight inference, cloud platforms perform large-scale model training and optimization, and user interfaces enable clinical decision support and feedback. Designing an effective HIoT framework requires addressing a multi-objective trade-off: maximizing accuracy (Formula presented) and stability (Formula presented) while minimizing latency (Formula presented) and energy (Formula presented), subject to constraints on model size (Formula presented) and robustness (Formula presented). To address this challenge, we propose HiPER, a hierarchical optimization-driven HIoT framework that jointly integrates acquisition, analytics, intelligence, and user interaction. To demonstrate its practical utility, HiPER is applied to monkeypox (Mpox) detection, referred to as HiPER-Mpox. In this framework, the edge employs lightweight inference with privacy-preserving transformations, while the cloud leverages transfer learning using a NASNetMobile backbone with squeeze-and-excitation channel recalibration to enhance accuracy and generalization. The user layer provides interpretable outputs and incorporates clinician feedback, improving trust and robustness. Evaluation on the Mpox Skin Lesion Dataset (MSLD) shows that HiPER-Mpox achieves 96% accuracy, 93% precision, MCC of 0.9145, and Kappa of 0.911, with an average per-image latency of 554 ms and a compact 2.07 MB edge model. These results demonstrate that the proposed HIoT framework satisfies the formulated optimization objectives while delivering a practical, interpretable, and resource-efficient solution for emerging healthcare challenges.