Online patient inquiries are often informal, incomplete, and written before professional assessment, yet they must still be routed to an appropriate level of clinical follow-up. We study this as a four-class actionable triage task -- self-care, schedule-visit, urgent-clinician-review, or emergency-referral, and ask whether prompted large language models (LLMs) can support such routing under low-resource labeling conditions. Using the public HealthCareMagic-100K corpus, we construct a 300-example human calibrated gold evaluation set, a 700-example auto-labeled silver training set, and a 40-example few-shot pool. We compare Term Frequency-Inverse Document Frequency (TF-IDF) and Bidirectional Encoder Representations from Transformers for Biomedical Text Mining (BioBERT) baselines train on silver labels against six prompted LLMs under 0-shot, 4-shot, and 12-shot conditions respectively. Accordingly, we evaluate with macro-$F_1$ alongside safety-aware metrics, including emergency-recall, under-triage rate, and severe under-triage rate. The strongest LLM (Claude Haiku 4.5, 12-shot) reaches macro-$F_1$ 0.475, exceeding the best supervised baseline (BioBERT, 0.378) on point estimate, with overlapping confidence intervals. Few-shot prompting and two-model agreement help in label-dependent ways: self-care agreement is reliable, urgent-clinician-review is not. We conclude that LLMs can support triage prioritization and selective human review, but not autonomous deployment.