Anja, I have to take a low dose of Iodine or I get hypothyroid symptoms very strongly. I'm not surprised since my body is very sensitive to all things. I find I do well on 4-6 mg a day and I do much better when I take the selenium at the same time. I also take Vit C and magnesium off and on. To me, it sounds like that may be the case with you. If you want to experiment and see if that's what's happening taking a break with no Iodine or kelp at all for a few days to a whole week would probably be an indicator. And from there you could start with a low dose and hold for 3 days and see how you feel. We are all different and finding the right dose can seem like a lot of work since it's trial and error.
I did find when I felt fatigued sometimes drinking a protein shake would help (not soy). And don't forget your B vitamins too, especially if you're having hypo symptoms.
Hope you get to feeling better soon.
Take care.