I’ve had acne on again off again (mostly on) since I was a teenager (30 years ago).
The best thing for me has been using a bar soap in the shower with hydrogen peroxide.
I’ve been using a 10% version from Coral Actives for the last year or so, and it’s cleared up 95% of my trouble spots without drying my skin out.
I do avoid dairy, too… but I’ve been allergic to cows milk pretty much since I was born, so that’s nothing new for me.