Messaging patients is a critical part of healthcare communication, helping to improve things like medication adherence and healthy behaviors. However, traditional mobile message design has significant limitations due to its inability to explore the high-dimensional design space. We develop PAME-AI, a novel approach for Patient Messaging Creation and Optimization using Agentic AI. Built on the Data-Information-Knowledge-Wisdom (DIKW) hierarchy, PAME-AI offers a structured framework to move from raw data to actionable insights for high-performance messaging design. PAME-AI is composed of a system of specialized computational agents that progressively transform raw experimental data into actionable message design strategies. We demonstrate our approach's effectiveness through a two-stage experiment, comprising of 444,691 patient encounters in Stage 1 and 74,908 in Stage 2. The best-performing generated message achieved 68.76% engagement compared to the 61.27% baseline, representing a 12.2% relative improvement in click-through rates. This agentic architecture enables parallel processing, hypothesis validation, and continuous learning, making it particularly suitable for large-scale healthcare communication optimization.