This paper presents the first large-scale study of the prevalence of misinformation related to opioid use disorder (OUD) on YouTube. In collaboration with clinical experts, we validated eight common misinformation categories and released a dataset of expert-labeled videos. To achieve efficient labeling, we introduced a classification pipeline called MythTriage, which uses lightweight models to handle common cases and delegates difficult cases to a high-performance, yet expensive, large-scale language model (LLM). MythTriage achieved a macro F1 score of up to 0.86 and is estimated to reduce annotation time and financial costs by over 76% compared to expert and full LLM labeling. By analyzing 2,900 search results and 343,000 recommendations, we uncover how misinformation persists on YouTube, providing actionable insights for public health and platform moderation.