It is difficult to say whether the vitamins may cause an allergic reaction or not. The composition of the tablets are important here. On the other hand, it is likely that you may have cross-reaction with the different types of seaweeds.
Please consult your doctor to get further clarification.
I sure understand what you're asking here. I have often wondered the same thing after having such a terrible reaction to nori, which is used for sushi. People usually think I'm just being stubborn about trying sushi, because they think I don't understand that sashimi is totally different than sushi and sushi can be made without the raw fish. I know that, but it's the seaweed itself I'm very allergic to. One small taste of nori by itself made me instantly sick to my stomach years ago. Now, I steer clear of all seaweed, because I have good reasons to be concerned.
I'm also allergic to other types of seafoods, crustaceans in particular.
And, I always have the memory in the back of my mind of my own father nearly dying from an allergic reaction to the type of iodine used as a contrast dye to look at the heart muscle. At home when I was growing up, we had to use the low iodine formula of table salt that is found in the light blue canister. My father couldn't use sea salt, which my grandfather tried to prod him into. No, not after his doctor told him that he even had to be mindful of which table salt he was using. I seem to be fine with sea salt myself, though. It's tricky, because we do need a certain amount of sodium and iodine. I don't eat processed foods myself.