My school nurse looked at my sore throat saying I have mono or strep and my doctor said I have a sinus infection. Can someone explain this?

School nurses. School nurses are employed to help identify kids that need to be sent home to protect the student body from spread of contagious diseases.Any direct patient care is secondary to this first duty. They are not physicians & are not licensed to diagnose or treat your illness. In this case s/he correctly identified you as sick & potentially having a contagious illness. It's the doc's job to sort it out.
Need testing. A throat culture and perhaps a mono spot tes is in order to give you a definitive answer. If you have a post nasal drip from your sinuses it an give you a sore and red throat which may be viral in origin.