Seafood allergies cause many of the same skin and respiratory issues that other allergic reactions usually produce. Hives and rashes are common, as are breathing issues. Similar to other food allergies, digestive issues such as pain, diarrhea, and an upset stomach are regular. Seafood allergies also often bring swelling, which can occur in and around the mouth, on the face, and elsewhere on the body. In rare cases, a seafood allergy can become a serious anaphylactic reaction, which makes breathing difficult.