I'm not sure how quickly the rash/acne is appearing after eating, so I don't know if this is the same thing, but I'll throw in my experience....DD has had acne like what you describe (red w/ a whitehead in the center) since a couple days after birth. They're worse around her mouth, too. We've discovered that it's because she gets milk (or spitup) all around her mouth while she's eating, and if we're not really good about wiping it off well, and using a wet washcloth at least once a day, it gets worse. However, it isn't like the pimples show up minutes after eating....if that's what you're seeing, it's probably something different.
(Oh -- and mine had thrush too...she did start eating better after being on meds for a day, so I hope the same is true for you! Good luck!)
DD1 February 2012
DD2 July 2015