I am allergic to shellfish which are oddly not even a type of fish.
they aren't. Then what the heck are they?
Many types of shellfish are actually crustaceans which are closer to insects. There are other types as well.
Insects you say? oh my. I wonder if a bug tastes as good as a lobster.
They might taste similar since they are closely related, common ones that are eaten are shrimp, lobsters, crabs and crayfish. Crayfish remind me of insects a lot.
Maybe I should try that. What else do they have in common with insects?
They are invertebrates. They are both in the main class of the phylum Arthropoda so they are both arthropods which have an exoskeleton. 
I never knew that. You are just full of facts. 
Shellfish also includes cephalopods such as squids and octopuses, even though they don't really have a "shell".