What is she suffering from, because when she coughs, she also throws up the little food she has managed to eat. Is it the flu or something else exactly, please?

It is difficult to determine the exact cause of her symptoms without further information or a medical examination. It could be a flu or another respiratory infection. I recommend monitoring her symptoms closely and encouraging her to stay hydrated. If her condition worsens or if she has a fever for more than 72 hours, it would be advisable to seek medical attention from a doctor.