In this study, we present a novel approach for enhancing chest X-ray image classification (normal, Covid-19, edema, mass nodules, and pneumothorax) by combining contrastive learning and machine learning algorithms. A vast amount of unlabeled data was leveraged to learn representations so that data efficiency is improved as a means of addressing the limited availability of labeled data in X-ray images. Our approach involves training classification algorithms using the extracted features from a linear fine-tuned Momentum Contrast (MoCo) model. The MoCo architecture with a Resnet34, Resnet50, or Resnet101 backbone is trained to learn features from unlabeled data. Instead of only fine-tuning the linear classifier layer on the MoCo-pretrained model, we propose training nonlinear classifiers as substitutes for softmax in deep networks. The empirical results show that while the linear fine-tuned ImageNet-pretrained models achieved the highest accuracy of only 82.9% and the linear fine-tuned MoCo-pretrained models an increased highest accuracy of 84.8%, our proposed method offered a significant improvement and achieved the highest accuracy of 87.9%.