No, there is no need to have an empty stomach for the allergy testing. If the allergy test is performed on the skin, (skin prick test ot patch test) then it is important to make sure that the patient did not have antihistamine for minimum of 5 days prior to the test. for the blood test you do not need to be fasting and no need to stop the antihistamines. hope this clarify.
Both tests are important as they look at sensitisation from different angles. Sometimes we do both tests, but everything starts with consultation. We can test for more than 400 allergens and right selection of what allergens we are testing for can give information that help to make correct diagnosis and treatment