In this paper, we present a new approach about the integration Self-Supervised Learning with nonlinear Classifiers in Lightweight Swin Transformer (SSLnC-LSwinT) for improving performance of X-ray image classification. Our approach leverages unlabeled data to address the issue of labeled data scarcity in the medical field by using self supervised learning (SSL) to extract features. One of our key contributions is the introduction of the Lightweight SwinT architecture, a more lightweight variant of SwinT, designed to enhance computational efficiency, reduce model complexity, and shorten training time. To further improve  classification efficiency, we propose the integration of a nonlinear classifier instead of a linear classifier in Lightweight SwinT. The experimental results underscore our contributions, demonstrating significant reductions in model training time and notable improvements in classification performance. Our proposed method, which integrates SSL based on LSwinT with a nonlinear LightGBM classifier, achieves an accuracy of up to 87%, improving by 1.8% over the non-LightGBM SwinT version and reducing training time significantly (3:23:00 vs. 7:37:29) compared to the original SwinT architecture.