Yes.  In fact, in many cases of sinusitis in adults there is no
discharge through the nose at all.  Any infected mucus drains down the
back of the throat as post nasal drip.  That's been my experience.

The classic presentation of acute sinusitis that they used to teach in
medical school--thick discharge out one nostril only--is actually seen
more in children than adults.

Of course, there could be something else wrong with you altogether.  But
whatever it is, is unlikely to be *caused* by a problem with your front
teeth.  (If you had said side molars rather than front teeth, that would
be a different story.)