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Here is an overview from the Mayo Clinic.
One of the biggest problems with shellfish allergic people is getting products that are contaminated with shellfish. Although in theory, the kelp and chondroitin should be all right to use with your allergy, there are risk factors involved.
Fortunately, Iodine requires very little supplementation and that can be gotten through the use of iodized table salt in normal amounts used to season your food.