The COVID-19 pandemic has affected all aspects of society, bringing health hazards and posing challenges to public order, governments, and mental health. This study examines the stages of crisis response and recovery as a sociological problem by operationalizing a well-known model of crisis stages in terms of a psycho-linguistic analysis. Based on an extensive collection of Twitter data spanning from March to August 2020 in Argentina, we present a thematic study on the differences in language used in social media posts and look at indicators that reveal the distinctive stages of a crisis and the country response thereof. The analysis was combined with a study of the temporal prevalence of mental health related conversations and emotions. This approach can provide insights for public health policy design to monitor and eventually intervene during the different stages of a crisis, thus improving the adverse mental health effects on the population.