Large Language Models (LLMs) have shown strong performance on static medical Question Answering (QA) tasks, yet their reasoning often deteriorates in multi-turn clinical dialogues where patient information is scattered across turns. This paper introduces TriMediQ, a triplet-structured approach that enhances the reasoning reliability of LLMs through explicit knowledge integration. TriMediQ first employs a frozen triplet extraction LLM to convert patient responses into clinically grounded triplets, ensuring factual precision via constrained prompting. These triplets are incorporated into a patient-specific Knowledge Graph (KG), from which a trainable projection module consisting of a graph encoder and a projector captures relational dependencies while keeping all LLM parameters frozen. During inference, the projection module guides multi-hop reasoning over the KG, enabling coherent clinical dialogue understanding. Experiments on two interactive medical QA benchmarks show that TriMediQ achieves up to 10.4\% improvement in accuracy over five existing baselines on the iMedQA dataset. These results demonstrate that structuring patient information as triplets can effectively improve the reasoning capability of LLMs in multi-turn medical QA.