This paper introduces a self-learning agent that integrates LLaMA 3.2 with a Progressive Neural Network (PNN) for continual learning in conversational AI and code generation. The framework dynamically collects data, fine-tunes tasks with minimal samples, and leverages Meta-Learning for rapid adaptation. LoRA optimizes fine-tuning, while Elastic Weight Consolidation (EWC) enhances knowledge retention. Experimental results demonstrate improved adaptability and memory stability, positioning this approach as a scalable step toward Artificial General Intelligence (AGI).