Distributed controllers in software-defined networking (SDN) become a promising approach because of their scalable and reliable deployments in current SDN environments. Since the network traffic varies with time and space, a static mapping between switches and controllers causes uneven load distribution among controllers. Dynamic migration of switches methods can provide a balanced load distribution between SDN controllers. Recently, existing reinforcement learning (RL) methods for dynamic switch migration such as MARVEL are modeling the load balancing of each controller as linear optimization. Even if it is widely used for network flow modeling, this type of linear optimization is not well fitted to the real-world workload of SDN controllers because correlations between resource types are unexpectedly and continuously changed. Consequently, using the linear model for resource utilization makes it difficult to distinguish which resource types are currently overloaded. In addition, this yields a high time cost. In this paper, we propose a reinforcement learning-based switch and controller selection scheme for switch migration, switch-aware reinforcement learning load balancing (SAR-LB). SAR-LB uses the utilization ratio of various resource types in both controllers and switches as the inputs of the neural network. It also considers switches as RL agents to reduce the action space of learning, while it considers all cases of migrations. Our experimental results show that SAR-LB achieved better (close to the even) load distribution among SDN controllers because of the accurate decision-making of switch migration. The proposed scheme achieves better normalized standard deviation among distributed SDN controllers than existing schemes by up to 34%.