Excessive smartphone use and dependence on social media give rise to multiple issues that negatively affect the overall well-being of individuals. Nomophobia is characterized as a "digital disease" due to the unlimited use of smartphone devices. The aim of this study is to examine smartphone use and social media involvement in association with nomophobia and psychological traits (i.e., depression, anxiety, stress, and self-esteem) of young adults. A cross-sectional investigation was conducted on 1408 Greek undergraduate students aged 18 to 25 years, using an anonymous self-reported questionnaire. Study data were collected through the Nomophobia Questionnaire (NMP-Q), Depression Anxiety Stress Scale (DASS-21), and Rosenberg Self-Esteem Scale (RSES). Participants' social media engagement was summarized through four variables: use of social media applications, number of friends, number of followers, and number of messages exchanged daily on social media. High levels of nomophobia were associated with high engagement in social media and, thereby, with a high number of friends. The same applies to participants with high/normal self-esteem compared to those with low. Regarding stress, anxiety and depression were not associated with digital network use, while elevated stress and anxiety seemed to play a negative role in the number of online followers. In addition, high levels of anxiety were correlated to an increased number of messages exchanged through social media applications.