In response to your ? re: coughing and headache.....yes, I have brought on (just the other day) a whopper of a headache. It started with a sneeze where my eyes felt as though they were bulging from their sockets, to waking in the middle of the night for no reason (means head pain soon come), then by morning felt swelling sensation in occiput region and wham--major head pain. Took ibuprofen (800 mgs plus 400 mgs before bed). This seemed to remedy the monster. Days before this headache I brought on similar one while coughing due to inhaling liquid down the windpipe. This one did not roar it's ugly head past 30 minutes.
I heard at the recent Symposium from Dr. Silberstein (spelling ?) expert in field of headaches, coughing, sneezing, exercise induced headaches can be sign of CSF pressure problem or perhaps Chiari I syndrome. I have not seen anyone as of yet for this problem as I am awaiting response from doc regarding another problem. One problem at a time is all I can handle now as I'm in Germany until mid September visiting our daughter and son-in-law and their, "Ahem, our new grandaughter!"