In today's digital age, video content is prevalent, serving as a primary source of information, education, and entertainment. However, the Deaf and Hard of Hearing (DHH) community often faces significant challenges in accessing video content due to the inadequacy of automatic speech recognition (ASR) systems in providing accurate and reliable captions. This paper addresses the urgent need to improve video caption quality by leveraging Large Language Models (LLMs). We present a comprehensive study that explores the integration of LLMs to enhance the accuracy and context-awareness of captions generated by ASR systems. Our methodology involves a novel pipeline that corrects ASR-generated captions using advanced LLMs. It explicitly focuses on models like GPT-3.5 and Llama2-13B due to their robust performance in language comprehension and generation tasks. We introduce a dataset representative of real-world challenges the DHH community faces to evaluate our proposed pipeline. Our results indicate that LLM-enhanced captions significantly improve accuracy, as evidenced by a notably lower Word Error Rate (WER) achieved by ChatGPT-3.5 (WER: 9.75%) compared to the original ASR captions (WER: 23.07%), ChatGPT-3.5 shows an approximate 57.72% improvement in WER compared to the original ASR captions.