3 months after a total thyroidectomy and my doctors are still struggling to get my levels within range. Could this be causing my constant dizziness?

Levels after... This is unusual but not unheard of. Your thyroid levels being too high or too low could cause the symptoms you report. You may be the uncommon patient who needs their thyroid replacement in an un standard way. Examples include: changing the brand of your T4, being given a combo of T4 and T3, (liothyronine) or using a desiccated thyroid preparation.