With the rapid expansion of unstructured clinical texts in electronic health records (EHRs), clinical named entity recognition (NER) has become a crucial technique for extracting medical information. However, traditional supervised models such as CRF and BioClinicalBERT suffer from high annotation costs. Although zero-shot NER based on large language models (LLMs) reduces the dependency on labeled data, challenges remain in aligning example selection with task granularity and effectively integrating prompt design with self-improvement frameworks. To address these limitations, we propose OEMA, a novel zero-shot clinical NER framework based on multi-agent collaboration. OEMA consists of three core components: (1) a self-annotator that autonomously generates candidate examples; (2) a discriminator that leverages SNOMED CT to filter token-level examples by clinical relevance; and (3) a predictor that incorporates entity-type descriptions to enhance inference accuracy. Experimental results on two benchmark datasets, MTSamples and VAERS, demonstrate that OEMA achieves state-of-the-art performance under exact-match evaluation. Moreover, under related-match criteria, OEMA performs comparably to the supervised BioClinicalBERT model while significantly outperforming the traditional CRF method. OEMA improves zero-shot clinical NER, achieving near-supervised performance under related-match criteria. Future work will focus on continual learning and open-domain adaptation to expand its applicability in clinical NLP.