Biomedical entity linking aims to map nonstandard entities to standard entities in a knowledge base. Traditional supervised methods perform well but require extensive annotated data to transfer, limiting their usage in low-resource scenarios. Large language models (LLMs), especially closed-source LLMs, can address these but risk stability issues and high economic costs: using these models is restricted by commercial companies and brings significant economic costs when dealing with large amounts of data. To address this, we propose “RPDR”, a framework combining closed-source LLMs and open-source LLMs for re-ranking candidates retrieved by a retriever fine-tuned with a small amount of data. By prompting a closed-source LLM to generate training data from unannotated data and fine-tuning an open-source LLM for re-ranking, we effectively distill the knowledge to the open-source LLM that can be deployed locally, thus avoiding the stability issues and the problem of high economic costs. We evaluate RPDR on two datasets, including one real-world dataset and one publicly available dataset involving two languages: Chinese and English. RPDR achieves 0.019 Acc@1 improvement and 0.036 Acc@1 improvement on the Aier dataset and the Ask A Patient dataset when the amount of training data is not enough. The results demonstrate the superiority and generalizability of the proposed framework.