Hi So Posh!
It does make sense that with your Taurus Sun in the Sixth House, you would have environmental energies. You need a good environment surrounding you to make you feel healthy.
Per Jan Spiller, coughs are the domain of Pisces, so you may want to see what Uranus (the modern ruler) and Jupiter (the traditional ruler) are doing in your chart natally, by transit and by both secondary and solar arc progresssions. If you do not live in your birth city, run a relocation chart and see what impact the city's energy has on you.
Coughs are usually trying to bring up something to clear it out of the lungs, throat or, in rare cases, through the breathing passages (think of getting water up your nose and you will see what I mean). When one is coughing due to a cold, it is to clear congested mucus or irritants from the lungs. When one is choking, one coughs to clear the foreign object from the throat.
Physically, I would look around not just my interior home environment but also what type of businesses, construction and traffic patterns surround my home. For example, if you live within a half-mile radius of a freeway and close to busy streets, you could be getting not only particulate pollution from the exausts but street "dust" from the wearing away of the pavement, remanents of any construction being done on the freeway or city streets, etc. If have windows open while you sleep (especially in the late spring, summer and early fall), this particulate pollution can get into the airways and the body automatically tries to clear it out. It is easier for the body to "breathe" it out during the day because it is not in a prone position, which it is at night when you sleep. The body has to work harder at night to clear it out, hence the cough.
Psychologically, the purpose of the cough would be the same. If there is something that a person has kept inside for long enough and it no longer serves the person, the body will want to release it. Since most coughs are related to the lungs and airways, what type of Gemini things are you consciously or unconsciously holding onto that your body is trying to clear out? Thought patterns that no longer serve you? All work and no play? Look at what is in Gemini and its aspects to natal, transiting and progressed planets and the house(s) it is on the cusps of in your chart so you can intentionally start releasing whatever it is and clearing the cough.
Hope this helps...