I inhaled a fragment of a tree nut. i can feel it in my chest. coughing (when i inhale) has made it go farther down. what should i do?

I recommend going to the hospital emergency room where prompt evaluation is obtainable to determine whether the fragment seems to be lodged in the bronchial area and poses danger of significant respiratory tract inflammation. If you're having symptoms, get checked. A chest xray or CT scan may be ordered. And a thoracic surgeon can be consulted if deemed advisable.