A recent rise in online content expressing concerns with public health initiatives has contributed to already stalled uptake of preemptive measures globally. Future public health efforts must attempt to understand such content, what concerns it may raise among readers, and how to effectively respond to it. To this end, we present ConcernScope, a platform that uses a teacher-student framework for knowledge transfer between large language models and light-weight classifiers to quickly and effectively identify the health concerns raised in a text corpus. The platform allows uploading massive files directly, automatically scraping specific URLs, and direct text editing. ConcernScope is built on top of a taxonomy of public health concerns. Intended for public health officials, we demonstrate several applications of this platform: guided data exploration to find useful examples of common concerns found in online community datasets, identification of trends in concerns through an example time series analysis of 186,000 samples, and finding trends in topic frequency before and after significant events.