Social appearance anxiety is a type of social anxiety that is associated with body image perception and exacerbated by the use of social media, leading to feelings of loneliness. The purpose of this cross-sectional study was to examine the relations between social appearance anxiety, use of social media, and feelings of loneliness in Greek adolescents and young adults. The sample of the research consisted of 632 participants, 439 women (69.5%) and 193 men (30.5%), aged 18–35 years. The Social Appearance Anxiety Scale (SAAS), the Social Media Disorder Scale (SMDS), and the UCLA Loneliness Scale were the instruments used. Data collection was performed online, via Google forms. Multiple regression analyses were performed and demonstrated a significant positive correlation between the Social Appearance Anxiety Scale and the UCLA Loneliness Scale scores. The feeling of loneliness was predicted by the social appearance anxiety score (p < 0.0001). On the other hand, there was a significant negative correlation between the Social Appearance Anxiety Scale and the Social Media Disorder Scale scores (p = 0.002), suggesting that social media use may exacerbate appearance anxiety and, hence, loneliness. The findings suggest that there may be a complex, vicious reverberatory cycle between appearance anxiety, use of social media, and feelings of loneliness in some young people.