Large language models (LLMs) have been increasingly adopted to support patients' healthcare-seeking in recent years. While prior patient-centered studies have examined the capabilities and experience of LLM-based tools in specific health-related tasks such as information-seeking, diagnosis, or decision-supporting, the inherently longitudinal nature of healthcare in real-world practice has been underexplored. This paper presents a four-week diary study with 25 patients to examine LLMs' roles across healthcare-seeking trajectories. Our analysis reveals that patients integrate LLMs not just as simple decision-support tools, but as dynamic companions that scaffold their journey across behavioral, informational, emotional, and cognitive levels. Meanwhile, patients actively assign diverse socio-technical meanings to LLMs, altering the traditional dynamics of agency, trust, and power in patient-provider relationships. Drawing from these findings, we conceptualize future LLMs as a longitudinal boundary companion that continuously mediates between patients and clinicians throughout longitudinal healthcare-seeking trajectories.