When I cough there is a tingling feeling in the middle of my chest. What could it be?

Possibilities... This is possibly due to a musculoskeletal problem. Possibilities include muscle strain, cartilage inflammation, etc. The possible diagnoses of the cough include bronchitis, bronchospasm, gerd, sinus disorders, etc. See your doctor for a more specific diagnosis.
Allergy. Pleural irritation most likely due o allergy.