There are people who have headaches after talking on the phone - googling that you get lots of hits, so it sounds like an allergic reaction might not be out of the question.
My guess is you should probably get a hands free wireless device and give up talking on that phone. Although, 40 minutes seems like an excessive amount of time to be on the phone so maybe limiting your calls to a couple minutes and doing most of your socializing face to face might work too.
Best wishes.
This might sound silly, but have you tried disinfecting the phone itself? I have read that phones are a HUGE carrier of germs, and have gotten in the habit of sanitizing my phone at least once every 2 or 3 days. I also sanitize door handles and our remote, fridge handle. I'm not ocd or a germophobe by any means, but once I started thinking about things we'd touch and then touch the aforementioned items, It really grossed me out! But, if this doesn't help your issue, maybe talk to an allergist? Even the receptionist might have some answers for you or advice about what you should do! Hope this helps!