Like many types of pests, roaches shed various things, such as feces and saliva. It’s the protein in their waste and body parts that can be a year-round allergen for some people. If you have asthma or believe you are allergic to cockroaches, your physician may recommend that you get a blood test or skin prick test to confirm whether you are allergic. Talk to your doctor about ways to help reduce the symptoms of a cockroach allergy.