I had a tooth extracted which led to dry socket. The dentist treated it w/ antibiotic and it sealed up. Quickly after I got a cold with the most rotten tasting/smelling mucus (so bad other can smell it) accompanied, by intermittent headache, slight fever, nausea (from swallowing it I anticipate) & stuffed up nose only in the nasal passage over the tooth extraction site. OTC meds only make me feel better for a little bit at a time. HELP!
Hi. Once the tooth has been taken out of the oral cavity and any complication like Chat Doctor.  It may be most likely a coincidental problem. Moreover if you still suspect, the tooth to be a reason for all this, you may ask the dentist to take a X-ray of that area, to make sure, nothing remains inside the extraction socket. Now Foul smelling mucus and stuffed nose can be treated with inhalation of steam along with warm saline gargle and antibiotics for a few days.