You'll be just fine and your Doctor can most likely provide you with something light to ease the anxiety in the days before. Keep in mind that MILLIONS of people go under general anesthesia in a year with only the very very very very rare side effect. I've only heard of the things you mention via news but have never personally known someone who has had an issue.
I'm the "orthopedic poster child" and have been under GA six times for different accidents/surgeries as well as when I was diagnosed with Melanoma and had that surgery. It's a very simple procedure; you get an IV, get a little "happy juice" squirted in via the IV, they ask you to count backward from 10 and well, I've never made it past six as far as I know. You wake up a little sleepy in a nice warm blanket with a slightly dry mouth.
Also, the anesthesiologist will consult with and interview you prior to the procedure and you'll have an opportunity to express and discuss your concerns. Whoever your surgeon is, it's in their best interests as well to suggest a good person to handle it so they do their work and look like a Rockstar when it's done.