Large Language Models (LLMs) hold considerable promise for healthcare applications, leveraging vast, diverse datasets to deliver insights across a broad range of tasks. However, their effectiveness in personal health settings is currently limited by their dependence on unstructured information, leading to issues concerning accuracy, trustworthiness, and personalization. In this perspective, we propose a transformative framework integrating Knowledge Graphs (KGs) and Causal Graphs (CGs) with LLMs to tackle these challenges. KGs contribute structured, verifiable knowledge that grounds LLM outputs in validated information, while CGs delineate causal relationships that are crucial for precise health assessments and intervention planning. This integration directly addresses these limitations for enhancing the potential of LLMs in personalized health scenarios. We also discuss potential practical and computational challenges that must be addressed to realize this integration in real-world applications.