While Large Language Models (LLMs) have demonstrated strong zero-shot reasoning capabilities, their deployment as embodied agents still faces fundamental challenges in long-horizon planning. Unlike open-ended text generation, embodied agents must decompose high-level intents into actionable sub-goals while adhering to the constraints of a dynamic environment. Standard LLM planners frequently fail to maintain strategy coherence over extended horizons due to context window limitations or hallucinate state transitions that violate environment constraints. We propose GiG, a planning framework that structures embodied agents' memory using a Graph-in-Graph architecture. Our approach employs a Graph Neural Network (GNN) to encode environmental states into embeddings, organizing these embeddings into action-connected execution trace graphs within an experience memory bank. GiG enables retrieval of structurally-similar priors, allowing agents to ground current decisions in relevant past structural patterns. Furthermore, we introduce a bounded lookahead module that leverages symbolic transition logic to enhance the agent's planning capabilities through grounded action projections. We evaluate our framework on three embodied planning benchmarks-Robotouille Synchronous, Robotouille Asynchronous, and ALFWorld. Our method outperforms state-of-the-art baselines, achieving Pass@1 performance gains of up to 22% on Robotouille Synchronous, 37% on Asynchronous, and 15% on ALFWorld while maintaining comparable or lower computational cost.