Background and Objectives: Mental health disorders are often the consequence of hormonal disorders such as those accompanying polycystic ovary syndrome (PCOS), where changes in appearance and having to deal with a number of other problems occur due to this illness. The objective of this study was to determine the prevalence and severity of anxiety and depression symptoms, the level of ego-resiliency, and the ways that women with PCOS cope with stress compared to healthy women in order to determine the influence of socio-demographic characteristics in relation to levels of anxiety and depression with ego-resiliency and stress-coping methods. Materials and Methods: The study was conducted in Poland in 2021 and included 230 women with PCOS and 199 healthy controls aged 20–40 years old. The hospital anxiety and depression scale (HADs), ego-resiliency scale, as well as the MINI-COPE inventory were used. Results: The women with PCOS had higher levels of anxiety and depression and poorer ego-resiliency in comparison to the healthy women. The women with PCOS used passive stress-coping strategies significantly more commonly than the healthy women. Living in rural areas, having a lower level of education and being childless increased anxiety levels. Similarly, being over 30, living in a rural area, having a lower level of education, being childless, and being obese increased depression levels in the women with PCOS. A low level of ego-resiliency and passive stress-coping strategies are predictors of high levels of anxiety and depression in women with PCOS. Conclusions: Women with PCOS should be checked for anxiety and depression. They should also be checked to see whether they have the resources to cope with chronic stress in order to optimize therapeutic interventions.