Public health measures were among the most polarizing topics debated online during the COVID-19 pandemic. Much of the discussion surrounded specific events, such as when and which particular interventions came into practise. In this work, we develop and apply an approach to measure subnational and event-driven variation of partisan polarization and explore how these dynamics varied both across and within countries. We apply our measure to a dataset of over 50 million tweets posted during late 2020, a salient period of polarizing discourse in the early phase of the pandemic. In particular, we examine regional variations in both the United States and Canada, focusing on three specific health interventions: lockdowns, masks, and vaccines. We find that more politically conservative regions had higher levels of partisan polarization in both countries, especially in the US where a strong negative correlation exists between regional vaccination rates and degree of polarization in vaccine related discussions. We then analyze the timing, context, and profile of spikes in polarization, linking them to specific events discussed on social media across different regions in both countries. These typically last only a few days in duration, suggesting that online discussions reflect and could even drive changes in public opinion, which in the context of pandemic response impacts public health outcomes across different regions and over time.