Re: kids feel sick
There's a slight AmE/BrE difference there. In BrE, if I say "I feel sick", it does mean that I feel as if I might vomit. If I have a headache or stomach ache or have the flu etc, I say "I feel ill".
If a child is lactose intolerant, then ingesting milk can have a few different effects - a rash, a runny nose, feeling nauseous and/or throwing up. In the context of the passage though, I would read "some kids feel sick" to mean "some kids feel as if they are going to vomit". Some them actually do vomit.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.