Sentiment analysis is a crucial NLP task used to analyze opinions in various domains, including marketing, politics, and social media. While transformer-based models like BERT and SBERT have significantly improved sentiment classification, their effectiveness in low-resource languages remains limited. Tamil and Tulu, despite their widespread use, suffer from data scarcity, dialectal variations, and code-mixing challenges, making sentiment analysis difficult. Existing methods rely on traditional classifiers or word embeddings, which struggle to generalize in these settings. To address this, we propose a hybrid framework that integrates fine-tuned SBERT embeddings with a Multi-Layer Perceptron (MLP) classifier, enhancing contextual representation and classification robustness. Our framework achieves validation F1-scores of 0.4218 for Tamil and 0.3935 for Tulu and test F1-scores of 0.4299 in Tamil and 0.1546 on Tulu, demonstrating its effectiveness. This research provides a scalable solution for sentiment classification in low-resource languages, with future improvements planned through data augmentation and transfer learning. Our full experimental codebase is publicly available at: github.com/ciol-researchlab/NAACL25-Mystic-Tamil-Sentiment-Analysis.