He needs to drink much more liquid then he normally does, eating Watermelon
is good too. This will help to flush out the toxins.
Also make sure he is not constipated - that can cause Acne
too for the same reason as not drinking enough water: the toxins are not being transorted out fast enough.
Just try to see what happens, hopefully he will be fine in couple of days.
I agree with Gita, he needs to know that it's all good to do cleanses and as soon as all that junk is gone, he will feel better and look better. So don't ever feel bad wanting the best for your kid. :)
And a personal experience: eating lots of carbs (for me it was tons of pasta...) and sweets made my skin brake out like never before and I'm not a teenager...