Ive had 4 in total, with 3 being as an adult. I had the canula inserted, then the anaesthetist spoke to me whilst the anaesthetic was administered - asked me if I was okay, how I was feeling etc. I remember there being a funny taste in my mouth/throat (which they assured me was fine), then the next thing was waking up in recovery. I am always really, really cold after a GA, and need extra blankets (or, after a knee surgery, an amazing warming thing that was like a hose that blew warm air - under the bottom of the covers and it was lovely!).
When I was in recovery from my last GA (gallbladder removal), I had chest pain and was crying because of it. The recovery nurse asked why I was crying, to which I replied, “because my chest hurts!!” They did an ECG there and then, which was fine, it was where air was trapped after the procedure (my gallbladder proved stubborn and difficult to get out, which meant there was a bit more air than usual). But the nurses were on it and making sure I was okay, without crowding, if that makes sense? Once we all knew I wasn’t having any cardiac events, they left me mostly alone until was taken back to the ward.
YANBU to be worried, but as someone said, it’s easier to worry about the anaesthetic than the procedure. Try to remember you wouldn’t be having it if it wasn’t necessary, and that the surgical team are highly trained.