The structure of this sentence is incomprehensible
Hurting is what her throat is doing to her, and she is coughing.
Doesn't French have a similar structure? "Sa gorge lui fait mal (à elle)" (with indirect "lui" like "al ŝi").
So, could you also say "Doloras ŝin la gorĝo, kaj sxi tusas"?
I was having trouble remembering that "tusi" means "cough", but found a helpful mnemonic. Robitussin is an antitussive (anti-cough) medicine.