If you started having palpitations after increasing to 100 mcg, it probably wasn't the fault of your dose. It could have been due to nutritional deficiencies - which meant that your body couldn't handle the increase - or adrenal fatigue. But the NHS doesn't believe in nutrition, nor in adrenal fatigue, so they wouldn't have tested for either.
That doctor sounds like a bit of a... ignoramous. There was no need to remove your gland. What was his justification for that? But, they just know nothing about it, so I suppose he panicked and that was the only thing he knew how to do. It's such a shame.
Radioactive iodine is usually used for cancer or people with Graves Disease who cannot be helped by medication. I have Hashi's, so I don't know a lot about it. But I do know that a) 100 mcg is just a starter dose, really; b) Hashi's people swing from hypo to hyper and back again, and the hyper state is transitory, it doesn't last long, and you end up with no gland and hypo, if measures aren't taken to stop the antibody activity. I don't know if that is any consolation. But, I also know that c) doctors know nothing about any of that!
What were your blood test results at that time, do you remember? Removing the gland is what doctors think is the easy solution - for them, not the patient! Trouble is, they have no idea how to correctly treat the patient after the gland has gone.
It is never good to 'diet'. Calorie-counting is artificial and counter-productive. People go on about the Paleo diet is the natural way to eat. But people in Paleolithic times didn't count calories! lol Of course, they didn't have the temptations we have today, but even no... cutting out the fat in order to eat a cream cake is not the way to go. (And, believe me, I've done that, and been there. I remember calculating that is I didn't put butter on my toast, I could have jam! lol But, that was a long time ago...) You will always put the weight back on if you do it that way. A balanced diet, and a sensible way of eating for life is the best way to do it.
But, don't beat yourself up about it. I doubt if there's any long-term damage done. But, from now on, count nutrients, not calories, and concentrate on getting your thyroid hormones right. The rest should take care of itself.