Is he lactose intolerent?

please help im having problems with my 9 mth old. i couldnt feed from birth as i had not enough milk, the first formula was fine until 6 months old his face and arms started going all red. the 2nd formula i tried he started throwing up all food and milk (projectile vomiting), got diarrhea and the doc said he was dehydrated from it. now he is on soy milk and he is fine. however i picked him up from daycare last week and he had red spots around his mouth, and the only thing different they gave him was a cheese sandwich. how do i tell what is wrong with him?