Zinc Causing Nausea

I've been taking Iodine and all the cosupplements suggested for about two weeks now. I have hashimotos, so I was also taking the zinc supplement (zinc sulfate), but after about a week of the supplements I started getting very sick when taking the supplements. I rotated/eliminated until I discovered it was the zinc making me sick, to the point of throwing up.

I always make sure I eat before taking the supplements and that doesn't help.

Does anyone have a solution for this? Does anyone know what causes this? Is the zinc absolutely necessary?