This always is one of those amorphous issues. You have a cough. Doctors test you in all manner of ways and can't find the cause. One thing that you shouldn't overlook is the anastrozole (or any of the AIs) as cough can be an adverse effect from it (and most doctors are not tuned into the gzillion effects which the AIs can manifest in different people. And, if you're like me, your high blood pressure med (and others) may have a similar effect. When you look drugs up on the web, the manufacturers rarely mention cough… instead, look each one up by inputting, for example, "anastrozole and cough," etc. and voila! Mayo also is a good resource for looking up adverse effects of various drugs, and drug interactions.
The second aspect of this issue is, what can a patient do about it? Your oncologist, for example, might say that it's just one of those trade-offs for taking an AI and not worth stopping the AI… and s/he has a good point, which is why many of us keep a big supply of sugar-free cough drops on hand.
My experience with the entire breast cancer journey is that my body/health likely will never be the same; weird things will arise, may come and go, and it behooves me to research them and take them all in stride. In the meantime, I send you blessings.