Surgery is scary. Find out as much as you can about it. If it is a routine surgery, then the team has obviously perfected it at this point. If it is a rare surgery, then you are being seen by a specialist who knows what they are doing.

GooleWithers is right. Learn about it. These days, the anesthesiology team and surgeons are very advanced in technology; they know what to do and also what to do if anything goes awry. You can tell your doc about the anxiety; maybe he'll give you a few Anxiolytics meds to get you through the next few days. There's no shame in treating anxiety.

The problem with phobias and anxiety is that they don’t care about logic. I use a CPAP and, despite the entire purpose of the thing is to keep me breathing through the night, sometimes the claustrophobia kicks in and I feel like I’m being smothered. If you believe in God, I suggest you read and memorize Psalm 23. It’s turned out to be the best way I’ve found to calm my nerves.