We present MedCOD (Medical Chain-of-Dictionary), a hybrid framework designed to improve English-to-Spanish medical translation by integrating domain-specific structured knowledge into large language models (LLMs). MedCOD integrates domain-specific knowledge from both the Unified Medical Language System (UMLS) and the LLM-as-Knowledge-Base (LLM-KB) paradigm to enhance structured prompting and fine-tuning. We constructed a parallel corpus of 2,999 English-Spanish MedlinePlus articles and a 100-sentence test set annotated with structured medical contexts. Four open-source LLMs (Phi-4, Qwen2.5-14B, Qwen2.5-7B, and LLaMA-3.1-8B) were evaluated using structured prompts that incorporated multilingual variants, medical synonyms, and UMLS-derived definitions, combined with LoRA-based fine-tuning. Experimental results demonstrate that MedCOD significantly improves translation quality across all models. For example, Phi-4 with MedCOD and fine-tuning achieved BLEU 44.23, chrF++ 28.91, and COMET 0.863, surpassing strong baseline models like GPT-4o and GPT-4o-mini. Ablation studies confirm that both MedCOD prompting and model adaptation independently contribute to performance gains, with their combination yielding the highest improvements. These findings highlight the potential of structured knowledge integration to enhance LLMs for medical translation tasks.