That's not necessarily true. It's not a hard and fast rule. Labs vary all the time. Your numbers won't always be perfect; no one's will be. They fluctuate normally. I'd only be concerned about pre-diabetes if the number is consistently high, and your doc probably feels the same.
According to Google, an A1C up to 5.6 is normal. 5.7 is one-tenth of a percent higher. You're fine. I doubt anyone here has more expertise than your doc - a well educated and qualified medical professional. Google can't tell you either.
Well you did it though and that's Brill, don't downplay that, it's a big achievement. Practice makes perfect with this, habits do take a while to break but they can be broken not with force but with time, patience, courage and determination.
It's not silly thinking really, it's just anxiety driven skewed thinking. The assumption your mind is making is that the plane when in flight are dependant on your focus to keep it in the air and from something going wrong. It's akin to when your in the passenger seat in a car and you're scared to go to sleep because something might happen. The analysis is just a branch of your internal analysis, you just externalise it to include events and journeys etc. Fear based analysis.