So sorry to hear your DD is suffering, ask to be referred to a gastroenterologist and then ask about Intolerances (Fructose, Lactose, Sucrose, Glucose) and celiac..
Your DD's suffering sounds similar to my DD, we went through 2 years of my DD suffering very badly and all kinds of tests with no diagnosis , we too got the questions about school and is there anything happening at home etc. She was very poorly, she was eventually diagnosed with severe fructose and lactose intolerance.
Her symptoms were terrible stomach ache, reflux, headaches, dreadful gas and burping, diarrhoea & constipation, awful bad breath, very underweight but with a bloated stomach, really pale with black circles around her eyes.
I was eliminating foods, keeping food diaries but we were unable to pin anything down as being the cause, because as we now know fructose is in everything, so pretty much everything we were feeding her was causing her terrible problems, even the multi-vitamin I was giving her had fructose in it.
It was a gastroenterologist who eventually diagnosed her, the diagnostic tests were hydrogen breath tests. The blood test which the paediatrician did and ruled out lactose intolerance is apparently not a diagnostic test at all and same for celiac blood tests, only definitive test for celiac is an intestinal biopsy. If you are going to have her tested for celiac, do not remove gluten from her diet, she will have to be ingesting gluten to get a true negative or positive result
Within about 10 weeks of removing fructose & lactose from her diet, she was a different child and looks so very healthy now despite only being able to eat a very limited range of foods.
Good luck, I hope you get some answers, it is awful to see your little one suffering and not know what is going on..