Allergy testing is actually done using a blood sample or by placing tiny samples of allergens under the skin. The only thing a doctor could determine by swabbing your nose would be the presence of a bacterial infection, fungal infection or the presence of eosinophils which help indicate the presence of an allergic reaction (and cause inflammation).

If you're thinking that some substance you work with is causing an allergic reaction, standard allergy testing may not be much help - they typically only test for common environmental and food allergens and may not even have the allergen you're concerned about to test for.