Yes, small doses of kelp Iodine can cause detox but vomiting isnt usually one of them. Generally speaking kelp is a poor source of Iodine because the ocean is full of toxins and heavy metals.
Additionally doc in the know report it taking 6-12 MONTHS at 50mg a day to reach sufficiency, 400mcg a day and you will never get there.
Everyone is different hard to say what caused your tummy upset but a bunch pf supps at once can do it, hard to say which or if it was a combination in your case.
I would avoid ester-C if I were you, most people who arent supplementing dont get enough A, D and K to make sure calcium ends up where it needs to go so getting all that extra calcium from ester C over time will generally cause prolems in the form of soft tissue calcification.