Large Language Models (LLMs) have made remarkable advancements in the field of natural language processing. However, their increasing size poses challenges in terms of computational cost. On the other hand, Small Language Models (SLMs) are known for their efficiency, but they often struggle with limited capacity and training data, especially in specific domains. In this paper, we introduce a novel method aimed at improving SLMs in the medical domain using LLM-based generative data augmentation. The objective of our approach is to develop more efficient and capable models that are specifically tailored for specialized applications. Through experiments conducted on the PubMedQA dataset, we demonstrate the effectiveness of LLMs in refining and diversifying existing question-answer pairs. This refinement process leads to improved performance in a significantly smaller model after fine-tuning. Notably, our best SLM, with under 1.6 billion parameters, outperforms the few-shot GPT-4 on the PubMedQA dataset. Our code and generated data are publicly available to facilitate further explorations.