Nausea( feeling of vomiting) with pain abdomen for last three weeks must be investigated thoroughly. You have also mentioned that he is getting weaker.
It may be due to gastritis (stomach inflammation
), gastric ulcer, inflammation of liver, pancreas or other organs.
In case of lactose intolerance
the main symptoms are indigestion
, bloating, pain abdomen, may be associated with vomiting and nausea.
He also had headache earlier but this time you didn't mention that. As headache, pain abdomen and nausea may be a variety of migraine.
So I would suggest you to take it seriously and consult a pediatrician
for proper clinical evaluation.