Designing efficient evacuation networks is crucial for disaster preparedness, as poorly planned and managed evacuations can increase the time required for evacuees to reach safety zones or shelters, and potentially resulting in more casualties. Incorporating traffic considerations into evacuation network design and planning is essential to mitigate these risks. While some studies have estimated traffic congestion, few have integrated multiple aspects of evacuation planning, which is crucial for developing effective and realistic plans but leads to complex optimization problems. In this study, we propose and solve a mixed-integer programming model to address the Evacuation Network Design and Planning Problem under Traffic Congestion (ENDPPTC). Our model concurrently optimizes shelter locations, evacuation routes, and evacuee flows to minimize total evacuation time. Traffic congestion is modeled using a CTM-based formulation that accounts for time-varying road properties, multiple time periods, contraflow operations, and road segment capacities, ensuring a precise representation of traffic dynamics. To solve the ENDPPTC, we develop both exact and heuristic methods based on Benders decomposition. We also generate problem instances based on real-world network configurations to create representative and standardized benchmarks. Our computational results demonstrate that neglecting traffic congestion leads to inaccurate evacuation time estimates and significant delays, whereas incorporating contraflow operations significantly reduces total evacuation time.