I would take her to her physician as soon as you are able, it is certainly not healthy for her to keep coughing
and vomiting. The coughing
will hurt her insides if it is too strong and vomiting will prevent her from getting her much needed nutrients from food, etc.
I really am not able to tell you what it is, it could be a number of things, and, as I said, it would be best if she saw a doctor.
Please let me know the outcome, I know she must be miserable.