Chocolate has mostly Bromine, so it is the antidote to Iodine poisoning.
But poisoning is not the same as an allergic reaction.
Fluorine, chlorine, bromine, and iodine are all chemically very similar; they occupy the same group. They’re halogens and their outer valence shell is structurally very similar so they react chemically the same way. So, yes, I could certainly see where bromine would help with iodine poisoning, but it would not help with an allergy.
However, I’d expect that anyone sensitive to iodine would also react to fluorine, chlorine, and bromine.
I’m going to guess that pool water makes him break out, so I would avoid drinking tap water that has not been de-chlorinated, and that he can’t use fluoridated toothpaste. (I haven’t been able to use any toothpaste in well over a year)