Will a septoplasty stop me from constantly coughing up mucus?

It's unlikely.  You'll hopefully breathe better and may even have a more attractive look, however.

septoplasty fixes the structure of the nose, but does not change how your nose functions. If you have allergies or chronic sinusitis, septoplasty will not fix those problems. However, septoplasty can give you an opportunity to better treat those conditions with saline irrigation or topical steroids. Talk with your doctor!