I can't help with the insulin side of things, but when I started to take Thyroxine, many years ago now, everything started to 'wake up' inside me - my gut worked faster, kidneys went into overdrive for a few days, my hands and feet felt warm, hair and nails grew faster - all of that must have needed more energy, which of course for me just resulted in feeling hungry and eating more - but for all of that I would have needed more insulin, as it is involved in energy utilization ,
Low thyroid function is one of those things which creeps up - like old age beer and sugar - so you might have quite a bit of detoxing to do - and there will be tests and adjustments of doses in the future as you get back on track - but it would seem to be a perfectly normal thing to be happening and it is a pity no on e thought to mention that you'd probably see changes in energy requirement which are obviously quite significant for you.
I can only advise don't worry - just adjust to cope with the changes you see as they are to be expected in the circumstances.