Large Language Models (LLMs) such as GPT-4 and LLaMA have demonstrated remarkable reasoning abilities but require significant computational resources for fine-tuning. This paper presents a resource-efficient fine-tuning approach for LLaMA-3.2-3B to enhance medical chain-of-thought reasoning while operating under constrained GPU and memory settings. Using parameter-efficient tuning techniques such as LoRA and QLoRA, we adapt the base model on publicly available medical reasoning datasets. The model achieves improved reasoning coherence and factual accuracy while reducing memory usage by up to 60% compared to standard full fine-tuning. Experimental evaluation demonstrates that lightweight adaptations can retain strong reasoning capability in medical question-answering tasks. This work highlights practical strategies for deploying LLMs in low-resource research environments and provides insights into balancing efficiency and domain specialization for medical AI systems.