It is possible that the dentist overinstrumented the canal, may even
have entered the sinus.  However, while I'm sure it is possible, I've
never seen a sinus infection that I think can be legitimately traced to
endodontic treatment.
    One thing that can cause major damage is inadvertent extrusion of
irrigating fluid (sodium hypochlorite) past the tip of the root.  The
damage here though is usually very serious and immediate, so your
symptoms don't sound right.
    Of course it is possible that you have a sinus infection and the fact
that it happened at the same time as the root canal may be coincidence.
 Or you may have had a pre-existing sinus bug, and the additional
stress of the root canal stirred things up (here the overinstrumenting
may be significant).
    This is all speculation.  If the root canal looks OK at this point, I'd
go to my physician for evaluation, perhaps for a culture and
sensitivity.  Most sinus infections have a different microbial mix than
dental infections, so a culture may give you some clues as to causation,
but in any case should help in prescribing something that will deal with
the sinus.

Good luck,
Steve