Query optimization in big data analytics remains computationally expensive, particularly for resource-constrained environments where traditional optimizers fail to satisfy memory and latency constraints. We present an agentic query planning system that combines a rule-based teacher planner, UCB1 bandit exploration, cost-aware prediction, and knowledge distillation to a lightweight student planner. Our teacher planner generates SQL plans using six key optimization strategies, while UCB1 bandit search efficiently explores the plan space under explicit resource constraints. A Random Forest cost model predicts query latency from plan features, enabling cost-aware decisions. A distilled student planner (Logistic Regression or Gradient Boosting) learns to mimic teacher-bandit decisions for fast inference. Evaluation on NYC Taxi and IMDB datasets demonstrates 23% latency reduction compared to default planners while maintaining 94% constraint satisfaction. The student planner achieves 89% accuracy in replicating optimal plans with 15x faster inference time. Our single-file implementation enables reproducible big-data analytics on resource-limited machines and is publicly available at https://github.com/mahdinaser/agentic-kd-planner.