Background: Mental health deterioration in young adults in the aftermath of the COVID-19 pandemic is being increasingly studied. It is clear that the psychological consequences of the pandemic will be evident for many years, especially among the younger generation, who did not have time to acquire adaptive coping strategies before the outbreak of COVID-19. The purpose of this study was to assess the condition of the mental health of students at Polish universities after two years of the pandemic. The types of coping strategies used by the respondents to deal with stress were also evaluated in order to establish which of them could have a beneficial effect on the psyche of young people. Methods: This study included 721 participants (age [years]: M = 25.7, SD = 5.3; 269 (37.2%) males) recruited using snowball sampling from students at two universities in Lodz, Poland, and full-time doctoral students from across Poland (phase I of the study was conducted in March 2019 (N = 352); phase II of the study was conducted in April 2022 (N = 369)). The following tools were used in this study: The General Health Questionnaire (GHQ-28) by D. Goldberg, the Perceived Stress Scale (PSS-10), and the Inventory for Measuring Coping with Stress (Mini-COPE) by Carver et al. Pearson’s chi-square test and multivariate logistic regression were used in the statistical analysis. Results: The results detailing the condition of the mental health of the subjects, as measured using GHQ-28, were significantly worse in the group surveyed after two years of the pandemic than the results of the survey conducted in March 2019 (adjusted odds ratio for GHQ-28 ≥ 5: 3.66, 95%CI 2.12–6.30, p < 0.001). Statistically significant differences were seen for each of the subscales of the GHQ-28 questionnaire. Most often, the subjects complained of anxiety symptoms and sleep disorders, in addition to somatic symptoms. The risk factors for worsening mental health included female (odds ratio 1.70, 95%CI 1.20–2.40, p = 0.003) and professional inactivity (odds ratio 1.55, 95%CI 1.04–2.31, p = 0.031). On the other hand, the ages of the people surveyed, their relationship status, whether they had children, or the type of university they attended all proved to be insignificant. The following coping strategies had a positive impact on the mental health of the respondents: positive reframing (Z = −2.951; p = 0.003) and seeking emotional support (Z = −2.351; p = 0.019). In contrast, strategies such as self-distraction (Z = 2.785; p = 0.005), denial (Z = 2.948; p = 0.003), venting (Z = 2.337; p = 0.019), self-blame (Z = 5.511; p < 0.001) and behavioral disengagement (Z = 4.004; p < 0.001) were associated with poorer mental health among the respondents. Conclusions: 1. Of the students surveyed, 33% reported elevated stress levels after two years of the COVID-19 pandemic. 2. The overall mental health of students at Polish universities, as measured by GHQ-28, was significantly worse in the group evaluated after two years of the COVID-19 pandemic, mainly in respect of anxiety symptoms and sleep disorders. 3. Female gender and professional inactivity appeared to be risk factors for the students’ worsening mental health, which may be an indication of the need for further research and planning of psychotherapeutic interventions.