Sounds like you now have a sinus infection, and the infected phlegm is draining to your throat, causing the cough. If the antibiotics prove ineffective, a Sinus Flush will clear it out. Saline rinses are only useful in the lower sinuses.
http://www.medhelp.org/user_journals/show/2322
The Flip-Turn Sinus Flush is mildly risky, because you have to bend over to do it, preferably in a shower, but you can also do it outside on soft ground, or you can kneel down and lean over a bathtub with the shower running.
Also recommend visit to ENT.