I would say it's totally normal. it's a huge step in life, and I think we can all agree it would be amazing to achieve the results without actually having surgery but unfortunately... that's how it's gotta be done. I was pretty similar, but it seemed like I mellowed out just a few days before because it was like "okay, it's happening". Like you, I had never been under anesthesia, never had an IV, never had surgery, anything like that. I'm used to needles at this point though just from being on testosterone for three years.
I don't know if every doctor does this/how it varies, but my surgeon's staff made me feel extremely comfortable. Once they set me up on the table, they put this really cozy warm blanket over my torso, and I was already laying down when the anesthesiologist was getting the IV in. He said he was going to use one tiny needle to numb the area, then he was going to put the IV in. I barely felt the tiny needle and I didn't feel the IV go in, it kinda just felt like he put something on the top of my hand. Since I was already laying down I didn't need to see it go in or anything. I actually don't even remember falling asleep, I was really relaxed, I just remember waking up and rambling at the nurse about egg mcmuffins while she helped me dress. whoops
the important thing to remember is that this surgery has been done so many times, and it's going to be just fine! anethesgiologists are some of the most highly trained medical people out there and they are very precise, and should any problems arise the whole medical team knows what to do to make sure you are okay. as for the surgery part, it helped me to think that at least they weren't getting inside any important organ areas, it's pretty much just on the surface/outer area of your body. honestly, for me the most uncomfortable part was when the surgeon needed to draw all the stuff on my body beforehand, just because I don't like being touched there. If you are comfortable with how your surgeon is treating you I'm sure they will do their best to make you feel as comfortable and as at ease as you can. You'll be okay!!! it'll be worth it in the end.