Hello, and thanks for writing in.
There are many things that can cause these symptoms, such as a throat irritation, respiratory infection, eating something she shouldn't have, bronchitis, to name a few. I would not recommend inducing vomiting, since we don't even know if she ate something. Also, even if she did eat something, we don't know what it is, and if it would be safe to have her vomit out, such as something that may be rough or have sharp or pointy edges. Sometimes inducing vomiting can actually cause worse problems, which we definitely don't want to do. Since there are many things that can cause these symptoms, I would recommend just continuing to offer food and water and watch her closely. If the symptoms continue or worsen, then she should be examined to find out specifically what is causing her symptoms, so she can be treated appropriately.
I hope this helps. Let me know if I can assist you further.