Noisy labels can significantly impact medical image classification, particularly in deep learning, by corrupting learned features. Self-supervised pretraining, which doesn't rely on labeled data, can enhance robustness against noisy labels. However, this robustness varies based on factors like the number of classes, dataset complexity, and training size. In medical images, subtle inter-class differences and modality-specific characteristics add complexity. Previous research hasn't comprehensively explored the interplay between self-supervised learning and robustness against noisy labels in medical image classification, considering all these factors. In this study, we address three key questions: i) How does label noise impact various medical image classification datasets? ii) Which types of medical image datasets are more challenging to learn and more affected by label noise? iii) How do different self-supervised pretraining methods enhance robustness across various medical image datasets? Our results show that DermNet, among five datasets (Fetal plane, DermNet, COVID-DU-Ex, MURA, NCT-CRC-HE-100K), is the most challenging but exhibits greater robustness against noisy labels. Additionally, contrastive learning stands out among the eight self-supervised methods as the most effective approach to enhance robustness against noisy labels.