Ulcerative Colitis (UC) is an incurable inflammatory bowel disease that leads to ulcers along the large intestine and rectum. The increase in the prevalence of UC coupled with gastrointestinal physician shortages stresses the healthcare system and limits the care UC patients receive. A colonoscopy is performed to diagnose UC and assess its severity based on the Mayo Endoscopic Score (MES). The MES ranges between zero and three, wherein zero indicates no inflammation and three indicates that the inflammation is markedly high. Artificial Intelligence (AI)-based neural network models, such as convolutional neural networks (CNNs) are capable of analyzing colonoscopies to diagnose and determine the severity of UC by modeling colonoscopy analysis as a multi-class classification problem. Prior research for AI-based UC diagnosis relies on supervised learning approaches that require large annotated datasets to train the CNNs. However, creating such datasets necessitates that domain experts invest a significant amount of time, rendering the process expensive and challenging. To address the challenge, this research employs self-supervised learning (SSL) frameworks that can efficiently train on unannotated datasets to analyze colonoscopies and, aid in diagnosing UC and its severity. A comparative analysis with supervised learning models shows that SSL frameworks, such as SwAV and SparK outperform supervised learning models on the LIMUC dataset, the largest publicly available annotated dataset of colonoscopy images for UC.