(1) Background: Genetic hereditary hemorrhagic telangiectasia (HHT) is clinically diagnosed. The clinical manifestations and lack of curative therapeutic interventions may lead to mental illnesses, mainly from the depression–anxiety spectrum. (2) Methods: We report the case of a 69-year-old patient diagnosed with HHT and associated psychiatric disorders; a comprehensive literature review was performed based on relevant keywords. (3) Results: Curaçao diagnostic criteria based the HHT diagnosis in our patient case at 63 years old around the surgical interventions for a basal cell carcinoma, after multiple episodes of epistaxis beginning in childhood, but with a long symptom-free period between 20 and 45 years of age. The anxiety–depressive disorder associated with nosocomephobia resulted in a delayed diagnosis and low adherence to medical monitoring. A comprehensive literature review revealed the scarcity of publications analyzing the impact of psychiatric disorders linked to this rare condition, frequently associating behavioral disengagement as a coping strategy, psychological distress, anxiety, depression, and hopelessness. (4) Conclusions: As patients with HHT face traumatic experiences from disease-related causes as well as recurring emergency hospital visits, active monitoring for mental illnesses and psychological support should be considered as part of the initial medical approach and throughout the continuum of care.