Query optimization is a crucial problem in database systems that has been studied for decades. Learned query optimizers (LQOs) can improve performance over time by incorporating feedback; however, they suffer from cold-start issues and often require retraining when workloads shift or schemas change. Recent LLM-based query optimizers leverage pre-trained and fine-tuned LLMs to mitigate these challenges. Nevertheless, they neglect LLMs' in-context learning and execution records as feedback for continuous evolution. In this paper, we present SEFRQO, a Self-Evolving Fine-tuned RAG-based Query Optimizer. SEFRQO mitigates the cold-start problem of LQOs by continuously learning from execution feedback via a Retrieval-Augmented Generation (RAG) framework. We employ both supervised fine-tuning and reinforcement fine-tuning to prepare the LLM to produce syntactically correct and performance-efficient query hints. Moreover, SEFRQO leverages the LLM's in-context learning capabilities by dynamically constructing prompts with references to similar queries and the historical execution record of the same query. This self-evolving paradigm iteratively optimizes the prompt to minimize query execution latency. Evaluations show that SEFRQO outperforms state-of-the-art LQOs, achieving up to 65.05% and 93.57% reductions in query latency on the CEB and Stack workloads, respectively, compared to PostgreSQL.