(1) Background: Coronavirus disease, also called COVID-19, is a worldwide pandemic with a major impact on all aspects of the individual (health status, psychological, and economic aspects, among others). The perception of health professionals in this situation has been influenced by their economic and psychosocial situations. On the economic level, self-employed workers have no state subsidies, with the added disadvantage of not having sufficient means to cope with contagion. This could potentially have an impact on their health and indirectly on their family members, creating additional stress. The aim of this study was to determine whether there are differences in the level of anxiety of health professionals working in private practice compared to healthcare workers working in public institutions during the first three waves of COVID-19. (2) Methods: A cohort study on 517 subjects comparing anxiety between a group of health workers and a group of health professionals working in the public sector at three key moments during the pandemic was performed. (3) Results: Statistically significant differences were found between self-employed private health professionals compared to those working as public health workers. The perception of impact was worse in the self-employed; however, a higher level of anxiety was evident in public employees in all assessed domains (cognitive, physiological, and motor, p = 0.001). (4) Conclusions: There were significant changes when comparing the first phase between both groups; employed public healthcare workers manifested a sense of lower risk of COVID-19 contagion than privately employed professionals, who had a higher level of anxiety. In the second and third waves, negative feelings improved for both groups, and the fear of showing anxiety to the patient decreased over the course of the waves.