(1) Background: This study investigates the influence of social networks on young adults, focusing on both positive and negative impacts. It considers problematic social networking site use (PSNSU), emotional intelligence, empathy, and the phenomenon of Fear of Missing Out (FoMO). (2) Methods: A comprehensive online survey was conducted with 442 participants aged 18 to 30 years that used various psychometric tools to assess emotional intelligence, empathy, internet and social media use, and FoMO. (3) Results: The study revealed that young adults display low competencies in emotional intelligence and empathy, with a tendency towards problematic internet and social media use. High FoMO scores were observed, correlating with negative internet use outcomes. Gender differences in these aspects were also explored. (4) Conclusions: The findings suggest a complex interaction between social network use, emotional skills, and FoMO that impacts young adults' mental health and social behaviors. This study highlights the need for a nuanced understanding of these relationships and their implications for well-being and social interaction in the digital age.