Public health researchers are increasingly interested in using social media data to study health-related behaviors, but manually labeling this data can be labor-intensive and costly. This study explores whether zero-shot labeling using large language models (LLMs) can match or surpass conventional crowd-sourced annotation for Twitter posts related to sleep disorders, physical activity, and sedentary behavior. Multiple annotation pipelines were designed to compare labels produced by domain experts, crowd workers, and LLM-driven approaches under varied prompt-engineering strategies. Our findings indicate that LLMs can rival human performance in straightforward classification tasks and significantly reduce labeling time, yet their accuracy diminishes for tasks requiring more nuanced domain knowledge. These results clarify the trade-offs between automated scalability and human expertise, demonstrating conditions under which LLM-based labeling can be efficiently integrated into public health research without undermining label quality.