The COVID-19 pandemic has disproportionately impacted the lives of minorities, such as members of the LGBTQ community (lesbian, gay, bisexual, transgender, and queer) due to pre-existing social disadvantages and health disparities. Although extensive research has been carried out on the impact of the COVID-19 pandemic on different aspects of the general population's lives, few studies are focused on the LGBTQ population. In this paper, we identify a group of Twitter users who self-disclose to belong to the LGBTQ community. We develop and evaluate two sets of machine learning classifiers using a pre-pandemic and a during pandemic dataset to identify Twitter posts exhibiting minority stress, which is a unique pressure faced by the members of the LGBTQ population due to their sexual and gender identities. For this task, we collect a set of 20,593,823 posts by 7,241 self-disclosed LGBTQ users and annotate a randomly selected subset of 2800 posts. We demonstrate that our best pre-pandemic and during pandemic models show strong and stable performance for detecting posts that contain minority stress. We investigate the linguistic differences in minority stress posts across pre- and during-pandemic periods. We find that anger words are strongly associated with minority stress during the COVID-19 pandemic. We explore the impact of the pandemic on the emotional states of the LGBTQ population by conducting controlled comparisons with the general population. We adopt propensity score-based matching to perform a causal analysis. The results show that the LBGTQ population have a greater increase in the usage of cognitive words and worsened observable attribute in the usage of positive emotion words than the group of the general population with similar pre-pandemic behavioral attributes.