Background and Objectives: The ongoing COVID-19 pandemic has posed an array of new challenges for medical students worldwide. Amidst academic rigors, students are confronted with unique stressors, potentially affecting their mental health and substance use. This study aimed to investigate the multifaceted effects of depression, alcohol use, and stress on medical students and discern how these factors have been amplified by the pandemic’s circumstances, and to identify predictors of mental distress during the COVID-19 pandemic period. Materials and Methods: Two online anonymous and cross-sectional surveys were conducted at the University of Medicine and Pharmacy “Iuliu Hatieganu” in Romania among medical students in 2018 and in 2022. Data were gathered via online questionnaires distributed through closed student groups on social media platforms, with a total of 1061 participants, to investigate stress, depression, alcohol and drug use, and the impact of the pandemic and online education on mental health, maintaining anonymity and ethical approval. The Medical Student Stress Questionnaire (MSSQ) was employed to measure different aspects of stress, the Beck Depression Inventory (BDI) provided insights into the participants’ depressive symptoms, and for the assessment of alcohol consumption habits, the Alcohol Use Disorders Identification Test (AUDIT) was utilized. Results: Our findings showed a significant decrease in mean depression scores (13.81 vs. 11.56, with p < 0.001) from 2018 to 2022. In 2018, students scored significantly higher in the overall stress-related domains. Additionally, being female, facing financial constraints, and being in pre-clinical years emerged as predictors of heightened academic-related stress and depressive symptoms. Students who had experienced the loss of a family member due to COVID-19 exhibited a statistically significant rise in their average BDI score and current anxiety levels. Conclusions: The pandemic, despite introducing new stressors, may have indirectly fostered an increased focus on students’ mental health, leading to more refined support mechanisms. Specialized interventions, taking into account gender and financial problems, are needed to address the multifaceted challenges faced by medical students. Our study highlights the ongoing need to nurture both the academic and emotional strength of future medical practitioners.