Can you get her to rehearse coughing? Maybe talk about coughing and how it's just your body doing a normal thing, and then you coigh and get her to cough too. Tell her it's safe to cough and everyone does it. Then maybe teach her how to breathe deeply. My dd started deep breaths at 20 months and it's a great skill to calm her down during tantrums etc. Then when she coughs you could stay calm and tell her it's just her cough and to breathe deeply...

Good luck!