If your school accepted your application without IELTS, then I think you are fine. The embassy won't ask you for IELTS since it's not part of the requirements for admission. They will, however, assess your English skills during the interview.
Again as I said initially, it can literally take seconds for the embassy to verify if your program is taught entirely in English or not. You can print the course information from the school website just to be safe. If your program is truly taught entirely in English, then I think your admission letter alone will be enough. However, I suspect there might be another reason as to why your visa was rejected, so try to carefully assess your previous visa application again to see if there are other inconsistencies.