This might be related to the way in which you use your voice when you're on the phone. You might try a few sessions of voice therapy. A good voice therapist will be able to discover what you're doing with your voice when you're talking on the phone. He/she will be able to retrain you to speak more normally when on the phone. You may be straining your voice without realizing it.
Hi
I always cough after a minute or so on the phone. I have vasomotor rhinitus which means I cough under certain situations, cold, smoke, air fresheners, certain foods etc., and on the phone. If you have discovered why this happens, I,d be grateful for your thoughts.