Ds 2.5 also drinks coconut milk, we use this one:
m.tesco.com/mt/www.tesco.com/groceries/Product/Details/?id=271858837
we chose it because we didnt want to use soy & this was the one we found most closely resembles regular milk in appearance, smell & taste. Ds really likes it & didnt have a problem switching to it. Agree with pps on doing a total elimination diet, then you can be 100% sure if dairy is the culprit.
Fwiw my ds was covered head to toe with eczema, we cut dairy & within 2-3 weeks the eczema was completely gone. Now at 2.5 we find he can tolerate cheese really well, he can also have the occasional yoghurt but if he has one 2 days running he breaks out with a rash/eczema on his face & he has a loose bm. Cows milk causes similar reaction to yoghurt so we avoid it where possible.