You're describing very common symptoms for Covid long-haulers, and yes, it certainly affects the nervous system. I had extreme dizziness, fatigue, light-headedness, heart palpitations, tingling in the fingers, BP changes etc (though I tested negative for POTS).

Ironically, I had a car accident around the same time (March 2022) and my 3x per week chiropractic visits actually cleared up a lot of symptoms + extreme hydrations and other supplementation helped immensely too.