Hateful online content is a growing concern, especially for young people. While social media platforms aim to connect us, they can also become breeding grounds for negativity and harmful language. This study tackles this issue by proposing a novel framework called HOLD-Z, specifically designed to detect hate and offensive comments in Telugu-English code-mixed social media content. HOLD-Z leverages a combination of approaches, including three powerful models: LSTM architecture, Zypher, and openchat_3.5. The study highlights the effectiveness of prompt engineering and Quantized Low-Rank Adaptation (QLoRA) in boosting performance. Notably, HOLD-Z secured the 9th place in the prestigious HOLD-Telugu DravidianLangTech@EACL-2024 shared task, showcasing its potential for tackling the complexities of hate and offensive comment classification.