This work presents our participation in the EvalLLM 2025 challenge on biomedical Named Entity Recognition (NER) and health event extraction in French (few-shot setting). For NER, we propose three approaches combining large language models (LLMs), annotation guidelines, synthetic data, and post-processing: (1) in-context learning (ICL) with GPT-4.1, incorporating automatic selection of 10 examples and a summary of the annotation guidelines into the prompt, (2) the universal NER system GLiNER, fine-tuned on a synthetic corpus and then verified by an LLM in post-processing, and (3) the open LLM LLaMA-3.1-8B-Instruct, fine-tuned on the same synthetic corpus. Event extraction uses the same ICL strategy with GPT-4.1, reusing the guideline summary in the prompt. Results show GPT-4.1 leads with a macro-F1 of 61.53% for NER and 15.02% for event extraction, highlighting the importance of well-crafted prompting to maximize performance in very low-resource scenarios.