Applying while doing a PhD program at another university
Hi, I am an East Asian student and received a PhD offer from a university in the U.S. last February.
I completed both my bachelor's and master's degrees in my hometown and have never been to the U.S. before. I know very little about the U.S. and its PhD programs.
Last year I applied to several programs and there were three programs I really wanted to go to. One rejected me outright, another("School B" below) invited me for a Zoom interview, but the professor said they could not afford to take on another graduate student. The last one ("School C" below) admitted me with full funding.
School C is not well known in my country, whereas School B is very well known and highly ranked. One of my advisors who had taught me through my bachelor and master, suggested that I reapply to a more prestigious and highly ranked school, even though I was satisfied with my offer from School C.
However, I do not know much about the U.S., so I am not sure how to evaluate that advice. Frankly, I believe both schools would be excellent places for me to pursue my PhD. However, I am concerned about my future career prospects after graduation; also wondering whether reapplying during a PhD would be considered rude. If I reapply and am admitted elsewhere, would the faculty at School C feel offended or uncomfortable? Has anyone been in a similar situation?