The COVID-19 pandemic has affected all aspects of society, not only bringing health hazards, but also posing challenges to public order, governments and mental health. Moreover, it is the first one in history in which people from around the world uses social media to massively express their thoughts and concerns. This study aims at examining 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 a large collection of Twitter data spanning from March to August 2020 in Argentina, we present a thematic analysis on the differences in language used in social media posts, and look at indicators that reveal the different stages of a crisis and the country response thereof. The analysis was combined with a study of the temporal prevalence of mental health conversations across the time span. Beyond the Argentinian case-study, the proposed approach and analyses can be applied to any public large-scale data. This approach can provide insights for the design of public health politics oriented to monitor and eventually intervene during the different stages of a crisis, and thus improve the adverse mental health effects on the population.