Yes, it's possible to develop food allergies later in life. But there isn't a lot of research on the development of new food allergy in adults. Studies do show that respiratory allergies can develop later in life.
The severity of reaction due to a food allergy varies. Some reactions are mild — a little itching and a few hives. Other reactions are serious, including shortness of breath, swelling and fainting. It's impossible to predict the severity.
For this reason, don't ignore signs and symptoms such as those you describe. Shellfish are a common cause of food allergy. Allergic reactions are unpredictable, and subsequent reactions may be more serious. Until you can consult with an allergist, avoid all types of shellfish.