I am allergic to iodine, shrimp, lobster, seaweed, but can eat crab, fish clams, octopus. I would like to start taking fish oil for depression. Can I?

Allergy testing. It is unusual to be able to eat crabs and seafood with such a strong history of iodine and multiple seafood allergies. I would not recommend fish oil at this time. If you are depressed, there are medications and counseling that can help - see your Doctor. If you have not been evaluated for specific food allergies, seeing an Allergist for testing is advised.
Avoid fish oil. If you are seeking a non-prescription treatment, you do not have feelings of wanting to harm yourself, and your depression symptoms are of mild or moderate degree, then alternatives include regular exercise 30-60 minutes daily, and St. Johns Wort. These measures must always be accompanied, however, by counseling.