If anything is stuck in your respiratory system then the normal reflex is cough ,since you have no cough and all you tests are normal then you haven't to worry, no gum or anything there .your gum probably gone to the gastrointestinal system so don't worry .
some symptoms if aspiration had occured are:
-shortness of breath
-blue discoloration of the skin
-cough, possibly with green sputum, blood, pus, or a foul odor
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It is recommended that all individuals see a Family Doctor for a full medical examination annually. Adults should get their blood pressure checked (US Preventive Task Force), a flu vaccine (CDC) and more each year.