Hello,
FPIES is Food Protein-Induced Enterocolitis Syndrome. It is an immune reaction in the gastrointestinal system to one or more specific foods which is non IgE mediated and this may cause vomitings and diarrhea and hence stunted growth. Mostly caused by milk and soy formulas but solid foods can also cause it.
Avoidance of foods causing the symptoms is the key treatment. Avoidance of cereal grains, poultry and legumes is also recommended. However if the symptoms persist then take your child to ER immediately as he may need I/V fluids and management of shock.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.