This study investigates the relationship between self-reported psychological distress and emotions in social media posts, using a deep learning-based emotion analysis model. A cross-sectional design was used, collecting data from Instagram and Threads between June and September 2024. Social media users completed a survey assessing psychological distress, including depression, anxiety, perceived stress, and social isolation, and consented to the analysis of their textual posts. The emotion analysis model, based on KoBERT, classified seven emotions-happiness, sadness, anger, neutrality, anxiety, disgust, and surprise-in the text. Data from 87 participants and 2,610 sentences were analyzed using Pearson's correlation, t-tests, and ROC curves with SPSS software. Results showed a strong link between emotional expressions in posts and reported distress, with the most significant correlations involving happiness and sadness across all distress types. The model also demonstrated high predictive accuracy for psychological distress, with an AUC ranging from 0.845 to 0.924 (p < 0.001). These findings support the use of emotion analysis as a tool for early detection and monitoring of psychological distress through social media, highlighting its potential in mental health interventions.