What are the consequences of not treating sinus infection?
Letting a sinus infection "run its course" is actually the way most doctors handle shorter infections. Sinusitis that lasts less than 10 days is thought to be viral, and antibiotics are not effective against viral infections. Sinus infections running in the 2-3 week range are usually bacterial, but most infections will clear up on their own. Concerns about the development of antibiotic-resistant strains of bacteria (like MRSA) have made doctors and many medical organizations reluctant to prescribe antibiotics for shorter bouts of sinusitis, and getting a prescription in the early weeks is becoming less and less likely.
When an infection hits 3-4 weeks in duration, antibiotics are likely to be prescribed, but if the symptoms are mild or are improving, a doctor might still decide to let the infection run its course. If symptoms are severe (thick nasal discharge, facial pain, bad breath, loss of sense of smell, dental pain, etc.) then meds will likely be employed.
If a patient with severe symptoms at this point refuses to get medical attention, they may end up with several weeks (and even months) of continued discomfort. In rare cases infections can cause meningitis, infected clots can escape into the blood (if the infection gets particularly destructive), and even aneurisms or toxic shock can result.
The biggest concern is developing chronic sinusitis. If the infection lasts more than 12 weeks, it’s considered "chronic", but there’s another form that persists even after an infection has subsided. Usually referred to by it’s more formal name "chronic rhinosinusitis" (or "CRS" for short), it’s characterized by changes in the mucous membranes of the sinuses that make future sinus infections very likely.
Sinusitis that persists beyond 12 weeks is a good sign that CRS may already have taken hold. If an infection lasts this long a visit to an ENT (ears-nose-throat specialist) is a good idea; otherwise a lot more misery may be in the future.