In medical settings, it is critical that all who are in need of care are correctly heard and understood. When this is not the case due to prejudices a listener has, the speaker is experiencing \emph{testimonial injustice}, which, building upon recent work, we quantify by the presence of several categories of unjust vocabulary in medical notes. In this paper, we use FCI, a causal discovery method, to study the degree to which certain demographic features could lead to marginalization (e.g., age, gender, and race) by way of contributing to testimonial injustice. To achieve this, we review physicians' notes for each patient, where we identify occurrences of unjust vocabulary, along with the demographic features present, and use causal discovery to build a Structural Causal Model (SCM) relating those demographic features to testimonial injustice. We analyze and discuss the resulting SCMs to show the interaction of these factors and how they influence the experience of injustice. Despite the potential presence of some confounding variables, we observe how one contributing feature can make a person more prone to experiencing another contributor of testimonial injustice. There is no single root of injustice and thus intersectionality cannot be ignored. These results call for considering more than singular or equalized attributes of who a person is when analyzing and improving their experiences of bias and injustice. This work is thus a first foray at using causal discovery to understand the nuanced experiences of patients in medical settings, and its insights could be used to guide design principles throughout healthcare, to build trust and promote better patient care.