Have her try the Netti Pot or Ayr. They are nasal rinses that will help if it is either an infection or allergies - it probably won't cure it, but it will give her some relief until you can decide what to do. It is just a saline/salt water rinse, so you aren't adding any more medication to her system.
I prefer the Ayr because you squeeze it instead of pour it. The directions come in either box. Ayr is available at RiteAid and the Netti Pot at health food stores. Be sure it is a nasal wash and not just a mist. I started using these a lot when I was pregnant and my sinus issues got so bad. I just saw that she is 3 - these may be too much for her, but Simply Saline does have a wash too I think.
Good luck with your surgery decision, and sorry I can't be any help there.