Trying to explain what Noah has

FPIES is Food Protein-Induced Enterocolitis Syndrome

It is commonly pronounced "F-Pies", as in "apple pies", though some physicians may refer to it as FIES (pronounced "fees", considering food-protein as one word). Enterocolitis is inflammation involving both the small intestine and the colon (large intestine).

FPIES is a non-IgE mediated immune reaction in the gastrointestinal system to one or more specific foods, commonly characterized by profuse vomiting and diarrhea. FPIES is presumed to be cell mediated. Poor growth may occur with continual ingestion. Upon removing the problem food(s), all FPIES symptoms subside. The most common FPIES triggers are cow's milk (dairy) and soy. However, any food can cause an FPIES reaction, such as rice, oat and barley.

A child with FPIES may experience what appears to be a severe stomach bug, but the "bug" only starts a couple hours after the offending food is given. Many FPIES parents have rushed their children to the ER, limp from extreme, repeated projectile vomiting, only to be told, "It's the stomach flu." However, the next time they feed their children the same solids, the dramatic symptoms return.

What is Fructose Malabsorption?

Fructose malabsorption occurs when the amount consumed is more than can be absorbed by the small intestine. Unabsorbed fructose acts as an osmotic load with rapid movement into the colon, which can cause diarrhea. Bacterial fermentation of fructose in the colon results in gas formation and other gastrointestinal sympotms, such as abdominal pain, bloating, and nausea.

Symptoms of gastrointestinal distress occurring 30-180 minutes after consumption:
Abdominal pain, belching, bloating, flatulence, diarrhea, hausea, and tummy rumbling, depression, anziety, fatigue, headache, brain fog, either aversion to sweet-tasting foods or craving for sugar, weight loss and irritability.

Since fructose causes diarrhea, it flushes out some micronutrients from the small intestine before the are absorbed resulting in anemia and various other nutrient deficiencies.

And unfortunately Noah has both! So at the moment he is surviving on just Neocate which is an elemental formula and safe for both allergies.