Melissa,one thing I was told when my Rocky was vomiting and probably his meds came up too, was not to give him another pill.
Rocky drank a lot of water and often times it would come back up.
I never gave him anything other than his thyroidmeds.
Oh yes,I gave him some Slippery Elm,for diarreha(sp?).
Please don't think Rusty is dying:-(
Most HT cats eat a lot,are always hungry,but if you are certain she's not eating,hence lethargic,I would take her to the vet tomorrow morning.
I am not an expert like Growler and Sugar Cat Mom,I can only tell you about my experience with Rocky,he did not die from HT,but had a huge groth attached to his para-thyroid.
She is most likely dehydrated,we know ourselves how we feel after vomiting,you feel week and listless.
I am not sure how long a kitty can go without food or water,so I cannot answer you there..but I hope she's eating again
and
to you,it's heartbreaking to have to watch your kitty being sick...but I am sending lots of good vibes for her to get better