Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry for this concern for Baby Girl but it's certainly possible that this product is responsible for her illness depending on her symptoms.
Unfortuantely, depilatory creams such as Nair contain ingredients (Calcium hydroxide, for example) which can cause corrosive injury in the mouth, esophagus or stomach and could be quite serious depending on the amount which was ingested. If the patient vomits and inhales some of the material, then lung tissue can also be affected and aspiration pneumonia can develop.
If Baby Girl is showing gastrointestinal signs such as drooling, vomiting, disinterest in eating and/or lethargy or having a hard time breathing, then ingestion of this product may be why, I'm sad to say.
If that's the case, then I'd advise a vet visit as soon as possible.
If her signs differ from any of the ones I mentioned above, please let me know what they might be so that I can provide other possible explanations for them.
I hope this helps although I'm sorry that my response is not a more positive one. Deb