Humans are known to construct cognitive maps of their everyday surroundings using a variety of perceptual inputs. As such, when a human is asked for directions to a particular location, their wayfinding capability in converting this cognitive map into directional instructions is challenged. Owing to spatial anxiety, the language used in the spoken instructions can be vague and often unclear. To account for this unreliability in navigational guidance, we propose a novel Deep Reinforcement Learning (DRL) based trust-driven robot navigation algorithm that learns humans' trustworthiness to perform a language guided navigation task. Our approach seeks to answer the question as to whether a robot can trust a human's navigational guidance or not. To this end, we look at training a policy that learns to navigate towards a goal location using only trustworthy human guidance, driven by its own robot trust metric. We look at quantifying various affective features from language-based instructions and incorporate them into our policy's observation space in the form of a human trust metric. We utilize both these trust metrics into an optimal cognitive reasoning scheme that decides when and when not to trust the given guidance. Our results show that the learned policy can navigate the environment in an optimal, time-efficient manner as opposed to an explorative approach that performs the same task. We showcase the efficacy of our results both in simulation and a real-world environment.