Social isolation and school closure may predispose adolescents to higher prevalence rates of depression, anxiety, and stress. In this cross-sectional observational study, the validated Spanish version of the Depression, Anxiety, and Stress Scale was administered to 3112 students aged 14–22 years old. We also collected data on participant gender, age group, school shift (morning or afternoon), school year, family type, whether they or any first-degree relative had been infected with COVID-19, whether any family member had died of COVID-19, and whether either of their parents worked. Mean scores were 8.34 ± 6.33 for depression, 7.75 ± 5.89 for anxiety, and 10.26 ± 5.84 for stress. Female students presented significantly higher scores on all three measures compared with male students. Students who had been infected with COVID-19, who had an infected family member, or who had a family member who died of COVID-19 also presented higher scores on all three measures. Identifying the symptoms and warning signs of depression and anxiety disorders is critical, particularly in vulnerable populations like adolescents.