It is important for your surgeon and anesthesia provider to know you have this problem, and it does add some risk to anesthesia, but with proper precautions is typically readily dealt with. Good luck with your surgery.
It is acceptable to undergo a rhinoplasty even though you are having acid reflux. It is a good idea to address this with your physician anesthesiologist prior to surgery .They may elect to place a different type of breathing tube in your throat to prevent acid reflux during the surgical procedure. It is also important to check with your family doctor to get on anti-reflux medications prior to elective cosmetic surgery.