The COVID-19 pandemic forced countries all over the world to take unprecedented measures like nationwide lockdowns. To adequately understand the emotional and social repercussions, a large-scale reconstruction of how people perceived these unexpected events is necessary but currently missing. We address this gap through social media by introducing MERCURIAL (Multi-layer Co-occurrence Networks for Emotional Profiling), a framework which exploits linguistic networks of words and hashtags to reconstruct social discourse describing real-world events. We use MERCURIAL to analyse 101,767 tweets from Italy, the first country to react to the COVID-19 threat with a nationwide lockdown. The data were collected between 11th and 17th March, immediately after the announcement of the Italian lockdown and the WHO declaring COVID-19 a pandemic. Our analysis provides unique insights into the psychological burden of this crisis, focussing on: (i) the Italian official campaign for self-quarantine (#iorestoacasa}), (ii) national lockdown (#italylockdown), and (iii) social denounce (#sciacalli). Our exploration unveils evidence for the emergence of complex emotional profiles, where anger and fear (towards political debates and socio-economic repercussions) coexisted with trust, solidarity, and hope (related to the institutions and local communities). We discuss our findings in relation to mental well-being issues and coping mechanisms, like instigation to violence, grieving, and solidarity. We argue that our framework represents an innovative thermometer of emotional status, a powerful tool for policy makers to quickly gauge feelings in massive audiences and devise appropriate responses based on cognitive data.