I know this is an old post, but I came across it yesterday because I've been having this exact problem. For about two weeks I've had heartburn and especially for the past two days it's been awful - I've hardly eaten anything.
The answer for me was a bowl of Cheerios and milk. It was amazing! After not eating much for days, and feeling the constant burning, gross burping and feeling weak from poor nutrition, I felt 10 times better minutes after eating the first bowl. Then I got my appetite back and downed 3 more bowls last night! It is now the morning and I still feel better, going with another bowl instead of my usual breakfast, just to be safe.
Hope that helps someone out there!