It really doesn't sound as lactose intolerance. Viral diarrhea (Rotavirus) is common in children younger than 5 years, and some immunity develops after that, so it would be unusual to have 4 consecutive bouts of diarrhea from the virus.
What is the color and consistence of his stool? How many times a day? He is complaining (or you suspect) about school problems? Any abdominal pain, if yes, where exactly?
His stools are brown or sometimes brownish yellow and watery and he probable goes 6 times a day. He seems to mainly have abdominal pain in the morning when he is vomiting. If I push on his belly lightly he says it hurts mildly on the light side near the ribs, but not really anywhere else. There is not any shcool problems because we homeschool and he does well. We are actually on summer break. His doctor has placed him on the brat diet but we are on vacation so we will not be able to see him for several more days. Any insight will be appreciated.
Very roughly, I see three possibilities:
1. In food poisoning, vomiting is only the first few days, than diarrhea follows. Diagnosis is with a STOOL CULTURE TEST. Bacteria AND parasites should be checked.
2. Inflammatory bowel disease (Crohn's disease or ulcerative colitis) would go with eventual intestinal bleeding, low fever, tiredness. Beeing 11 is early for Crohn's anyway. Test is with colonoscopy/biopsy.
3. Liver and gallbladder are on the right side under the rib cage. ULTRASOUND can show gallstones, but it often miss them, so CT would be needed, or HIDA SCAN which shows gallbladder function. Yellow stool can indicate lack of bile in the stool, which is due to bile flow blockage somewhere in the biliary tree (stone, stenosis). Lack of bile in intestine causes that fats are not absorbed, and this causes diarrhea. Vomiting is often in gallblader/biliary duct disorders.
NOTE: BRAT diet is NO longer recommended in diarrhea. General opinion among doctors today is that anyone can eat what he wants and avoid only what obviously irritates him. Your son should maybe avoid fats when he has diarrhea.