Am I entitled to a refund if I'm not happy with my rhinoplasty?

In cosmetic elective surgery there are no Guarantees or Warrantees.No guarantee to satisfy patients perceived results.no refunds, partial or full.Any further surgery is the patient's responsibility 

The short answer is:  Probably not.
In general, surgeons make no guarantee as to results of surgery.  Many surgeons, however, feel that if a patient is unhappy with the result or if there is some deficiency in the result, some sort of concession is indicated.  In some cases, surgeons will make that known prior to surgery.  In my practice, we provide patients with some general written guidelines as to what can be expected if additional surgery is required.
Of course it is impossible to outline every situation, but cosmetic surgeons, in general, are very sensitive to having their patients satisfied with their results and will make every effort to see that they are.  However, from a purely technical aspect, it is very unlikely that you are entitled to a refund.

I am concerned about your statement regarding your surgeon's advice about taking out insurance to cover future revisions costs.  In nearly every situation, insurance would not cover a complication of cosmetic surgery unless the complication led to a functional impairment.

Hi and welcome to our forum!
The procedure of rhinoplasty requires the rental of an office space, the office staff to run it, supplies, an operating suite, its rental, an operating room staff, an anesthesiologist, operating facility supplies, etc., etc.  These are basic costs that cannot be avoided. 15% of cosmetic procedures require secondary touch ups. 
Surgery doesn't come with guarantees. The human body doesn't always cooperate with the gameplan. Scarring, bleeding, infection cannot always be prevented. Cartilage can warp, bone may shift.
In our practice, we heavily discount secondary touch up surgeries to cover our costs. 
Best wishes...