Is it possible to feel shaky and tired with normal blood sugar levels if you are use to having high blood sugar?

Yes. It takes time for your boby to adjust to a normal sugar level. That's why we always recommend a gradual approach rather than a quick fix.
Yes. Yes it can happen if your glucose readings has been previously running in the high 300s. This adjustment phase can last 2-3 weeks before your body gets used to the new and healthier glucose range you are currently having. Good job !