If its a contact rash, him wear long sleeves (light material of course) should help.

If to want to check if its the milk, find an area where there is no rash scratch the skin a little (not hurting, just like running a finger nail over.) then put a bit of milk in it. If it rashes its the milk causing it.
(That's a basic scratch test, an allergist would be able to tell for sure).

For myself I've avoided oat milk because I get hayfever rash/asthma from oat grass. I'm trying almond milk, starting this week.