The COVID-19 pandemic has brought unprecedented challenges, with a potential stress which might affect the education of resident doctors in the field of orthopedics and traumatology. Its repercussion on the residents’ strain and training routes is not well known. After two years of pandemic, this paper aims to analyze the repercussion of the coronavirus disease 2019 (COVID-19) on education, medical training, and the mental well-being of Romanian resident doctors in orthopedics and traumatology. In January–February 2022, an electronic questionnaire was distributed to all orthopedic resident doctors in the 12 residential training centers in Romania. Participants (n = 236) were resident doctors with an employment contract and professional activity during the COVID-19 pandemic. Resident doctors who did not work during this period were excluded. An online survey generator was used to electronically create the questionnaire. Statistical analysis was performed in Matlab version R2022a, with the support of Statistics and Machine Learning Toolbox Version 12.3. Descriptive statistics were performed for the standardized questions, while for the open questions, answers were collected by topic. The results of the Chi-square test indicate that there is a statistically significant association regarding the prevalence of infection among residents involved in the treatment of patients with COVID-19 (p = 0.028), and the influence of secondment in COVID-19 sections (p = 0.0003). The infection of residents is not related to their affiliation with a particular medical training center (p = 0.608), gender (p = 0.175), the year of study in residency (p = 0.733), the age group (p = 0.178), and the secondment period (p = 0.114). Residents who participated in the study had an overall well-being index of 13.8 ± 5.7, which indicates a low level of well-being for a large number of residents. Residents who would like to choose a new residency specialization, or would choose a non-medical career, had reduced average WHO wellness rates, as the risk of infection is associated with the treatment of patients with COVID-19 and secondment in COVID-19 sections. The findings of this study may help residency training centers to develop robust programs that can alleviate the impact of this pandemic. Some major changes will be needed to be integrated into residency training programs around the world. Emphasis should be placed on electronic educational portfolios, simulation of surgical processes, and distance learning, all of which have a high potential for health and safety, as well as for the moral support of residents.