(1) The COVID-19 pandemic has significantly affected the psychological well-being of people around the world. The aim of this study was to assess the levels of psychological distress of nurses (anxiety, depression, stress, insomnia) in relation to sociodemographic variables and psychosocial variables: self-assessment of health, quarantine, psychological support, presence of chronic diseases and the Impact of Events Scale (IES-R). (2) A total of 207 nurses working with COVID-19 patients at the Independent Public Clinical Hospital No. 1 of the Pomeranian Medical University in Szczecin participated in the study. The study was conducted with the diagnostic survey method, using the Athens Insomnia Scale, the Generalized Anxiety Disorder questionnaire, the Impact of Event Scale-Revised, the Patient Health Questionnaire-9, The Perceived Stress Scale and a questionnaire of our authorship. (3) Among the respondents, 40.58% suffered sleep disturbance, 36.71% had mild anxiety, 71.95% had high stress according to the PSS-10 and 31.88% had depression according to the PHQ-9. The study observed that the chances of insomnia decreased with the age of the respondents. Moreover, the form of employment of nurses significantly affected the levels of depression, anxiety and stress. (4) Education, gender and age were variables that significantly affected the severity of anxiety, depression and insomnia in the surveyed nurses working with patients with COVID-19.