I don't know if this helps, seeing as I'm a human and all, but I'm currently going through treatment for hyperT. When I was diagnosed i was very jittery, was quite thin, always sleepy, and had a heart rate that stayed around 110-120 resting. When they put me on treatment with PTU (maybe just a human drug?) They had me come in every 4 weeks or so for the first few months to have my blood tests looked at, but after that they spread them out to where I only had to come in every 3-6 months. Being a hyperT person stinks at times, but overall it's not too bad. I hope that sweet Peanut is a good kitty for her tests. You can feel quite rotten when your thyroid levels are elevated. But left untreated, it can get more serious and you could have bigger problems than her getting scared when it's time to go to the vet. But look at me- I'm hyper T and am alive, well, and am healthy enough to have gotten a hole poked through my tongue!
Best of luck and lots of comfort in this tough time for both you and your sweet little Peanut!