(1) Background: Physician rating websites (PRWs) are a rich resource of information where individuals learn other people response to various health problems. The current study aims to investigate and analyze the people top concerns and sentiment dynamics expressed in physician online reviews (PORs). (2) Methods: Text data were collected from four U.S.-based PRWs during the three time periods of 2018, 2019 and 2020. Based on the dynamic topic modeling, hot topics related to different aspects of healthcare were identified. Following the hybrid approach of aspect-based sentiment analysis, the social network of prevailing topics was also analyzed whether people expressed positive, neutral or negative sentiments in PORs. (3) Results: The study identified 30 dominant topics across three different stages which lead toward four key findings. First, topics discussed in Stage III were quite different from the earlier two stages due to the COVID-19 outbreak. Second, based on the keyword co-occurrence analysis, the most prevalent keywords in all three stages were related to the treatment, questions asked by patients, communication problem, patients’ feelings toward the hospital environment, disease symptoms, time spend with patients and different issues related to the COVID-19 (i.e., pneumonia, death, spread and cases). Third, topics related to the provider service quality, hospital servicescape and treatment cost were the most dominant topics in Stages I and II, while the quality of online information regarding COVID-19 and government countermeasures were the most dominant topics in Stage III. Fourth, when zooming into the topic-based sentiments analysis, hot topics in Stage I were mostly positive (joy be the dominant emotion), then negative (disgust be the dominant emotion) in Stage II. Furthermore, sentiments in the initial period of Stage III (COVID-19) were negative (anger be the dominant emotion), then transformed into positive (trust be the dominant emotion) later. The findings also revealed that the proposed method outperformed the conventional machine learning models in analyzing topic and sentiment dynamics expressed in PRWs. (4) Conclusions: Methodologically, this research demonstrates the ability and importance of computational techniques for analyzing large corpora of text and complementing conventional social science approaches.