Every day, patients access and generate online health content through a variety of channels, creating an ever-expanding sea of digital data. At the same time, proponents of public health have recently called for timely, granular, and actionable data to address a range of public health issues, stressing the need for social listening platforms that can identify and compile this valuable data. Yet previous attempts at social listening in healthcare have yielded mixed results, largely because they have failed to incorporate sufficient context to understand the communications they seek to analyze. Guided by activity theory to design HealthSense, we propose a platform for efficiently sensing and gathering data across the web for real-time analysis to support public health outcomes. HealthSense couples theory-guided content analysis and graph propagation with graph neural networks (GNNs) to assess the relevance and credibility of information, as well as intelligently navigate the complex online channel landscape, leading to significant improvements over existing social listening tools. We demonstrate the value of our artifact in gathering information to support two exemplar public health tasks: (1) performing postmarket drug surveillance for adverse reactions and (2) addressing the opioid crisis by monitoring for potent synthetic opioids released into communities. Our results across data, user, and event experiments show that effective design artifacts can enable better outcomes across both automated and human decision-making contexts, making social listening for public health possible, practical, and valuable. Through our design process, we extend activity theory to address the complexities of modern online communication platforms, where information resides not only in the collection of individual communication activities but also in the complex network of interactions among them.