The objective of the present study was to explore possible changes in the psychologicalwellbeing of young healthy students during the initial 14 days of the COVID-19 general lockdown that occurred in March of 2020, and if there was any relation with specific personality traits (neuroticism, psychoticism, and extraversion), cognitive styles (internal and external locus of control and intolerance of uncertainty), and coping strategies. One hundred twenty-two university students aged from 18 to 29 years participated in the study. The dispositional factors were assessed at the beginning of the study, while measures of psychological adjustment (anxiety, depression, and self-perceived health) were taken in three different assessment stages, employing validated questionnaires and scales. Anxiety and depression scores significantly increased after one week of lockdown, reaching a plateau pattern by the second week. The levels of self-perceived mental health, vitality, and quality of life showed a pattern of sustained progressive decrease, with a more acute lessening during the first week. Neuroticism, intolerance of uncertainty, and negative autofocus were associated to worse levels of psychological adjustment. These individual differences might be taken into consideration when designing prevention programs aiming to dampen the psychological impact of a general lockdown in healthy population.