The pandemic deeply changed young adults’ life. Lockdown period and the social restrictions dramatically affected university students’ mental health. The aim of our cross-sectional study was to describe psychological well-being, future anxiety (FA), and health complaints (HCs) in a sample of 3,001 students of the University of Florence in the middle of the first two pandemic waves. We assessed the role of subjective social status, chronic diseases, sense of coherence (SoC), and digital health literacy (DHL) as predictors of psychological well-being, FA, and HCs. Students expressed high levels of FA and reported being disturbed by not being able to achieve their desired future goals. About 40% reported a low or a very low well-being and 19.1% experienced two or more subjective health complaints more than once a week. The likelihood of having a better mental health status significantly increased with increasing SoC and among males. Subjective Social Status proved to be a predictor for FA. Enhancing SoC could improve the health status of the university students during the pandemic and beyond.