Social networks, particularly Twitter 9.0 (known as X as of 23 July 2023), have provided an avenue for prompt interactions and sharing public health-related concerns and emotions, especially during the COVID-19 pandemic when in-person communication became less feasible due to stay-at-home policies in the United States (U.S.). The study of public emotions extracted from social network data has garnered increasing attention among scholars due to its significant predictive value for public behaviors and opinions. However, few studies have explored the associations between public health policies, local political ideology, and the spatial-temporal trends of emotions extracted from social networks. This study aims to investigate (1) the spatial-temporal clustering trends (or spillover effects) of negative emotions related to COVID-19; and (2) the association relationships between public health policies such as stay-at-home policies, political ideology, and the negative emotions related to COVID-19. This study employs multiple statistical methods (zero-inflated Poisson (ZIP) regression, random-effects model, and spatial autoregression (SAR) model) to examine relationships at the county level by using the data merged from multiple sources, mainly including Twitter 9.0, Johns Hopkins, and the U.S. Census Bureau. We find that negative emotions related to COVID-19 extracted from Twitter 9.0 exhibit spillover effects, with counties implementing stay-at-home policies or leaning predominantly Democratic showing higher levels of observed negative emotions related to COVID-19. These findings highlight the impact of public health policies and political polarization on spatial-temporal public emotions exhibited in social media. Scholars and policymakers can benefit from understanding how public policies and political ideology impact public emotions to inform and enhance their communication strategies and intervention design during public health crises such as the COVID-19 pandemic.