Environmental leakage caused by varying carbon prices of different jurisdictions applied to the commonly shared transmission grid can negatively affect carbon emission reduction, air pollution exposure, and health implications for communities. Carbon border adjustment, as a set of constraints imposed on security-constrained economic dispatch, aims to address the environmental leakage by adjusting the dispatch outcomes. This paper presents a framework to assess the changes in air quality and health impacts of carbon prices and border adjustment once applied to the power systems. This is done by calculating the spatial distribution of pollutants based on the output of power system operations and linking it with the air diffusion and epidemiological modeling and mapping tool. We focus on three border adjustment schemes: non-border, one-way, and two-way models currently studied by various RTOs. The results are conducted on a grid with 10,0000 buses geographically encompassing the Western U.S. considering detailed data of generation emission and local socioeconomic conditions at county levels. Results show that individual communities can be impacted differently, even unfairly due to environmental leakage but the intensities can be reduced by appropriate employment of border adjustment. Thus, it is still important to complement carbon border adjustment with renewable energy investment for effective decarbonization and reducing inequity in air pollution exposure.