Protecting Moms and Babies Against Climate Change Act This bill establishes grants and directs other activities to address health risks associated with climate change, particularly for members of racial and ethnic minority groups, pregnant or postpartum individuals, and children younger than age three. Specifically, the Department of Health and Human Services (HHS) must establish a program to award grants to partnerships of community-based organizations and other entities to identify and address climate-change-related risks to these individuals at a county level. HHS must also establish a program to award grants to health professional schools and training programs to integrate training on identifying risks associated with climate change for patients, with a focus on those intending to become pregnant, in curricula and continuing education programs. In addition, the National Institutes of Health (NIH) must establish the Consortium on Birth and Climate Change Research. The consortium must coordinate research on climate-change-related risks conducted and supported by various NIH institutes and offices. The Centers for Disease Control and Prevention must also develop a strategy to identify areas where there is a high risk of adverse maternal and infant health outcomes due to climate change.