The first thing you need is a specific diagnosis. I have never seen, nor am I familiar with, a condition like the one you describe. Even people who think their acne is food-related--and most don't--do not describe the kind of immediate breakout you say you have.
So step one is to see a skin doctor. If you can provoke the rash, then eat a big fatty meal just before the visit. Just to be sure, take some good-quality photos of the spots in full bloom to the appointment.
In the event that you do have some fat reaction (and again, I've never seen or heard of this) then perhpas a dietititan can advise you on the kind of restrictive diet you may need.
Best.
Dr. Rockoff