Definitely sore muscles from coughing.
The big inhalations needed to produce a cough...as well as the muscles used in the coughing itself add up to thoratic fatigue.
I had either a severely pulled muscle once from a bad cough...or possibly even a minor cracked rib. The pain was suprisingly bad!
I say this not to worry you...but to let you know your sore back is to be expected. (I DO NOT think you've cracked a rib...just letting you know coughing is tough on the body sometimes!)
Hopefully you are able to knock off early and REST!!
Don't do anything when you get home...chores can wait.:)
Rest and recover!!