Hi, welcome to the forum, it is unusual that you are allergic to mint gum, but it can be possible. The symptoms may be suggestive of acute attack of asthma and hence a test with bronchodilators for 2-3 weeks will be useful to relieve the symptoms. If the symptoms don’t improve stop the medications.
The triggering factors like dust, fog, pollens etc. can cause the precipitation of these symptoms, apart from mint gum. Meantime avoid chewing mint gums.
Allergen-specific testing includes Skin testing, Serum tests for allergy, Allergen challenge and as well as Evaluation of respiratory system by spirometry will help to substantiate the diagnosis.
I suggest you to consult allergy specialist for further evaluation. Take care and regards.
you may be allergic to a specific ingredient in the brand of gum you chew not just the mint. read the ingredients and don't chew any more of that gum. if it happens with other things you eat talk to your doctor, you may have a food allergy.