Aussie,
I have had graves disease for about 16 years. Undiagnosed for about 5 the docs figure.
I thought it was normal to shake and be hyper. I thought that the fact that I was so active was the reason I was so thin also.
I had a thyroidectomy 11 years ago and the first few years on synthroid seemed to stabilize things.
Since I have had all of these maladies, they cannot figure out why my TSH jumps around so much, from hyper to hypo active. My heart rate is high most of the time and yes it is a strange sensation.
Some times when I am laying in bed it feels like the bed is moving because my heart beats so fast. I am sure it is not good for me, but it is just another thing that has to be addressed at Mayo.
If I went to the hospital every time I felt like I was having a heart attack I would be camped out at the ER.

I am so used to it know that I think I would know if it was a different kind of palpitation.
When I had a bout of hypertension and was on tenormin, that is when my heart rate was low and that was still around 80-90.
Hopefully, Mayo can tie everything together and have some answers.
Good luck to you,
Judy