The emergency department (ED) is a critical facility for unplanned care, handling patients without prior appointments. As patient volume increases, managing timely treatment becomes increasingly difficult, especially when prioritizing high-risk patients. This often leads to significant delays for those with less urgent conditions. In this paper, we propose a dynamic patient management approach aimed at minimizing wait times while ensuring timely care for both critical and non-critical cases. Our algorithm effectively reduces wait times for patients across all acuity levels and improves overall patient flow, while maintaining priority for those in the most urgent need of care. The results highlight the effectiveness of the proposed method in enhancing the efficiency and fairness of ED operations, demonstrating considerable improvements over traditional patient management algorithms.