My vertigo / dizziness was different; every day like if I was on a rocking boat. Related to a PTSD ( trauma approx 10 years ago ) After that it came back whenever a situation that triggered it. But gone now.
For me (before iodine) I was helped by taking loads of salt (himalayan) but not cured until Iodine and a host of other supplementation (vit B, C, potassium, magnesium +++) Some recommend start with adrenals before thyroid, it may be worth a try. I addressed them both at the same time and succeed, but I was on no medication.
What medication are you taking for tachycardia? Some of these may cause vertigo.. Medication in general is hard on the adrenals.
Palpitations, arrhythmia are connected to hypo thyroid as well; had it big time. It is like a puzzle, I had to start in one end and just find the pieces one by the other. Best of luck:)