Nurses face mental health issues like emotional labor, stress, and depression, increasing the risk of medical errors. This study assesses the mental health and medical errors among nurses in Korean medicine clinics in South Korea. The cross-sectional analysis involved 83 nurses, examining relationships between emotional labor, stress, depression, cognitive failure, Hwa-byung (HB) (a syndrome of suppressed anger in Korean culture), and medical errors. It identified factors associated with HB and medical errors using multiple regression analysis, presenting their odds ratios (ORs) with 95% confidence intervals (CIs). The findings revealed a current HB prevalence of 19.28% and a 6-month medical error prevalence of 16.87% among participants. The regression analysis showed that higher levels of depression (OR = 1.368, 95% CI = 1.098 to 1.703, p = 0.005), cognitive failure (OR = 1.072, 95% CI = 1.011 to 1.136, p = 0.020), and HB trait (OR = 1.136, 95% CI = 1.005 to 1.284, p = 0.041) significantly correlated with HB presence. This groundbreaking study on this previously under-researched nurse workforce highlights the critical need for comprehensive mental health care, with the objective of significantly enhancing their mental well-being and improving their overall work environment.