Literature data show that acute, severe, and also chronic stress play an important role in the development of somatic and mental disorders. It is well documented in the literature that starting university studies results in anxiety in many ways for individuals. In this present work, we examined how perceived stress affects the appearance of depression and sleep disorders among a special group: the first-year undergraduates. In February 2020, 134 students completed a 14-question Perceived Stress Scale questionarre. In addition, the 13-question Beck Depression Scale and the 8-question Athens Insomnia Scale were used as measures to assess their current mental health status. Following the outbreak of the COVID-19 pandemic, the extent to which anxiety and depressive symptoms changed had become a major issue worldwide. In June 2020, we repeated our previous measures in the given population with the same methods. Our research clearly proved higher perceived stress values among undergraduate students, which were associated with high depressive symptom parameters and insomnia. However, unexpectedly, questionnaires completed during the quarantine period of the COVID pandemic showed lower perceived stress, which was accompanied by a decrease in depressive symptoms and insomnia.