My blood type is RH - should I be scared or think twice about my upcoming surgery?

Your Rh blood type is not an issue. If you have concerns about bleeding, discuss with your surgeon in advance. 

Make sure you ask your surgeon this question.  In my practice, my concern about blood type only comes about when a transfusion may be possible (very rare).  If the surgery is extensive then you may donate your own blood and receive it after surgery.  Usually, this is done with insurance cases. If a blood transfusion is possible, then you may be able to stage the procedure and avoid the transfusion all together.  Not knowing what kind of surgery you are having makes it difficulty to answer.  Your Plastic Surgeon is the best resource to answer this question.