Clinical decision-making agents can benefit from structured reuse of prior decision experience. Motivated by illness scripts, we study how to organize clinical experiences with explicit applicability conditions and inter-experience relations. However, many memory-augmented methods store experiences as independent records without conditional or relational structure, which may introduce noisy retrieval, unreliable reuse, and in some cases even hurt performance compared to direct LLM inference. We propose GSEM (Graph-based Self-Evolving Memory), a clinical memory framework that formalizes experiences as indications and contraindications and organizes them into a dual-layer memory graph. GSEM captures both intra-experience decision structure and inter-experience dependencies, supporting applicability-aware retrieval and feedback-driven calibration of node quality and edge weights. Across MedR-Bench and MedAgentsBench with two LLM backbones, GSEM achieves the highest average accuracy among all baselines, reaching 70.90% and 69.24% with DeepSeek-V3.2 and Qwen3.5-35B, respectively. Code is available at https://github.com/unname797/gsem.