Some people with shellfish allergies also have reactions to medical iodine. It's probably worth getting that checked out. I have a shellfish allergy, but not the iodine reaction. I've also noticed that I have a hard time taking vitamins and some other medications. I've been told this is because some companies use ground shellfish shells as a filler. I've never done any research, so I'm not 100% sure this is true, but I do notice that my symptoms go away when I stop taking those pills.
It's true that they are often included, but not as filler. The reason they are put in is to add iodine or glucosamine sulfate to the nutrient mix; these are most concentrated in the shells rather than the flesh of the organism.
Most people with this allergy are not as careful as they probably should be about identifying WHICH shellfish they are allergic to. Shellfish is a common culinary name used for two completely different kinds of organisms: crustaceans and molluscs. MOST people who are allergic to "shellfish" are allergic to one but not the other (though some people are unlucky enough to be allergic to both), and it is really helpful to people who are trying to help you to know which allergen is the real culprit.
If you are allergic to crustaceans only, you can usually still eat things such as scallops or clams, but not such things as shrimp, lobster, crawfish, or crab. If you are only allergic to molluscs, you have to avoid scallops, clams, mussels, oysters and squid, but may be able to eat shrimp, for instance. (Yes, squid are molluscs; calamari counts.) I'm not actually allergic to any seafoods, but have a sensitivity to scallops; they make my throat itch. AFAIK, there is no other seafood product that is a problem for me.
(Which is a good thing; my extended family is in the business.)
The simplest way to avoid shellfish altogether when dining out or eating processed seafood products is to look for Kosher certification: Jews who keep Kosher can eat finfish but not crustaceans or molluscs.
If you can eat finfish, and want to, at an island destination, look for a place that specializes in broiling; they will normally be a bit more likely to be able to properly segregate shellfish from finfish unless the specialty of the house is lobster. Best bet is to buy it direct from the boat and cook it yourself, but look for a boat WITHOUT nets on booms; those will almost always be trawlers that pick up shellfish as bycatch even if they are not targeting it. Also, be careful of finfish species in the cod/hake family; they can have codworm, and codworm has chitin.
Also, be careful of fish sauce in asian restaurants; it is often thickened with ground crustacean shells. The usual allergen culprit in shellfish allergies is chitin, the protein that makes up crustacean shells; it can turn up as an ingredient in cosmetics as well as in nutritional supplements.
BTW for the OP, my good wishes for your child's continued good health, but my condolences on your loss of the beach as a happy place: beaches are not really safe for anyone who is allergic to mollusks, in particular, and if you have always been a beach person, having to give up those visits will be hard.