A lot of people I know have had very long and persistent coughs like that relatively recently. And similarly seems like there's "nothing wrong" (doctors can't find anything wrong) except that they just won't stop coughing. For the most part it has gone away by itself eventually though some people were stuck in a similar unfortunate situation to you where they were wiped out as well.
Sounds like you're at least on the mend, hope you're better soon :)