I had the same problem with a crown. My crown had been hurting for two weeks and everytime I would rub the gum right above the crown, it had a smell. Then i had a smell from my nose. I went to the dentist and the xray showed nothing just red tissue around gum. He did not want to replace the crown and gave me antibiotics. One week later, the smell got worse and my tooth got worse. I went to the endodontist who originally did the root canal and he said my tooth was for sure infected. Two of the roots in the tooth had infections above them. This was prob infecting my sinus and making my nose smell. I had an apioectomy done today and hope this will help. my nose has stopped smelling already but my gums are throbbing. I'm on bed rest for two days for sure. The procedure was not as bad as I thought. Make sure you brush, floss, and rinse twice a day and scrape any bacteria from your tongue. Go see an endodontist. Hope this helps.
Seeing a dentist is advised.