Online medical consultations generate large volumes of conversational health data that often embed protected health information, requiring robust methods to classify data categories and assign risk levels in line with policies and practice. However, existing approaches lack unified standards and reliable automated methods to fulfill sensitivity classification for such conversational health data. This study presents a large language model-based extraction pipeline, SALP-CG, for classifying and grading privacy risks in online conversational health data. We concluded health-data classification and grading rules in accordance with GB/T 39725-2020. Combining few-shot guidance, JSON Schema constrained decoding, and deterministic high-risk rules, the backend-agnostic extraction pipeline achieves strong category compliance and reliable sensitivity across diverse LLMs. On the MedDialog-CN benchmark, models yields robust entity counts, high schema compliance, and accurate sensitivity grading, while the strongest model attains micro-F1=0.900 for maximum-level prediction. The category landscape stratified by sensitivity shows that Level 2-3 items dominate, enabling re-identification when combined; Level 4-5 items are less frequent but carry outsize harm. SALP-CG reliably helps classify categories and grading sensitivity in online conversational health data across LLMs, offering a practical method for health data governance. Code is available at https://github.com/dommii1218/SALP-CG.