If your humidity in the house is too high and it is closed in, I would
be more suspicious of a high mold spore count causing sinus irritation
or worse a minor case of thrush in the sinuses and back of the throat.

Depending on where you live, U.S., there have been a couple of really
nasty cold viruses going around that will cause the same symptoms but
not develop into a full blown 2-4 week cold unless your immune system
gets hit with something else, like lack of sleep, etc.

My burning sinuses went away after I started using a steroid spray.
The first one I used was Nasalide.  There is Flonase and several others
that should be on a fromulary if you are on a HMO.

Was the onset sudden?  If so, it sounds like a mild flu.

I had one of those last winter.  It had all the symptoms of a cold
turning into a sinus infection, with one extra bonus--stomach upset
resulting in nausea and vomiting and fatigue.  I told my ENT about it
and he thinks I caught a very mild flu, just enough to trigger sinus
problems.  And it lasted for weeks.  Flu is viral so the antibiotic
won't help.  Be patient and wait till spring!