Hi: as mentioned, you have sore throat after long conversations causing cough.
There are usually 2- 3 causes
1) LPRD. It is larungi pharyngeal reflux
2) allergic ( as you have mentioned)
3) chronic laryngitis .
We need to examine throat for zeroing down to the conclusion
Next Steps
Take antiallergic and antacids for couple of week
Health Tips
Consume sips of water while having long conversation