In my case it does make it worse.
Like you I thought I had thyroid issues, but my tests were always normal, TSH of around 1.5 and 1. I started supplementing with iodine, and I got a lot worse, my TSH went to 4.5, I felt rotten.
I stopped the iodine, went on Armour (has T4 and T3) and got better. I was good for almost a year and then started adding kelp and coconut milk to my juice smoothies. I started getting hypothyroid symptoms again, I didn't get tested, but I stopped the kelp, felt better. I kept doing the coconut milk and juice smoothies and then after a month really didn't feel right, I felt hyper. I decided to go off my meds, and I felt a ton better. I realized that it was the coconut that was normalizing my thyroid!
Now I take 3 tsp coconut oil a day and am great. ALL my thyroid symptoms are gone.