Possible lactose intolerance

Patient: My son has been experiencing sickness for a while now however i have taken to docs and been advised this is probably just a bug from nursery. however i have monitored this and seems to me it is when he is having dairy. nursery have changed him to soya and i have reduced his dairy intake and he seems to have improved. however saturday he had abit more milk than usual and cheese spread sandwich and hes been sick since then. hes also been getting a rash on face and leg when he gets sick. could this be an intolerance to dairy?

Symptoms: Sickness, rash

Doctor: