After a cold or virus i experience an extreme tickling biting feeling in my stomach. it causes me to want to cough. it goes away after several weeks.

Inflammation: From your description here, it sounds like these viruses might be causing inflammation. This could persist for sometime giving you the sensation that u describe. This is especially true if you have asthma or someone in your family has it (which would give you a genetic link to the disease). Hopefully you have regular care with a primary doctor. If you have asthma, there are maintenance meds 2 take