Clinical antimicrobial therapy requires the dynamic integration of pathogen profiles,host factors, pharmacological properties of antimicrobials,and the severity of infection. This complexity imposes fundamental limitations on the applicability of Large Language Models (LLMs) in high-stakes clinical decision-making including knowledge gaps, data privacy concerns, high deployment costs, and limited reasoning capabilities. To address these challenges, we propose KRAL (Knowledge and Reasoning Augmented Learning), a low-cost, scalable, privacy-preserving paradigm that leverages teacher-model reasoning to automatically distill knowledge and reasoning trajectories via answer-to-question reverse generation, employs heuristic learning for semi-supervised data augmentation (reducing manual annotation requirements by approximately 80%), and utilizes agentic reinforcement learning to jointly enhance medical knowledge and reasoning while optimizing computational and memory efficiency. A hierarchical evaluation employing diverse teacher-model proxies reduces assessment costs, while modular interface design facilitates seamless system updates. Experimental results demonstrate that KRAL significantly outperforms traditional Retrieval-Augmented Generation (RAG) and Supervised Fine-Tuning (SFT) methods. It improves knowledge question-answering capability (Accuracy@1 on the external open-source benchmark MEDQA increased by 1.8% vs. SFT and 3.6% vs. RAG) and reasoning capability (Pass@1 on the external benchmark PUMCH Antimicrobial increased by 27% vs. SFT and 27.2% vs. RAG), achieved at about 20% of SFT's long-term training costs. This establishes KRAL as an effective solution for enhancing local LLMs' clinical diagnostic capabilities, enabling low-cost, high-safety deployment in complex medical decision support.