Recent advances in distributed learning systems have introduced effective solutions for implementing collaborative artificial intelligence techniques in wireless communication networks. Federated learning approaches provide a model-aggregation mechanism among edge devices to achieve collaborative training, while ensuring data security, communication efficiency, and sharing computational overheads. On the other hand, limited transmission resources and complex communication environments remain significant bottlenecks to the efficient collaborations among edge devices, particularly within large-scale networks. To address such issues, this paper proposes an over-the-air (OTA) analog aggregation method designed for the distributed swarm learning (DSL), termed DSL-OTA, aiming to enhance communication efficiency, enable effective cooperation, and ensure privacy preserving. Incorporating multi-worker selection strategy with over-the-air aggregation not only makes the standard DSL based on single best worker contributing to global model update to become more federated, but also secures the aggregation from potential risks of data leakage. Our theoretical analyses verify the advantages of the proposed DSL-OTA algorithm in terms of fast convergence rate and low communication costs. Simulation results reveal that our DSL-OTA outperforms the other existing methods by achieving better learning performance under both homogeneous and heterogeneous dataset settings.