I have known of people who had reactions to raising their FT3 level when their ferritin level was too low. It may be a stretch to assume that is the cause of your heartburn, but it is worth a try. If you want to do that, supplement with iron for long enough to get your ferritin to at least 100 and then try again with the T3 med.
That is what I intended to suggest. Sorry it was not clear. Taking the iron supplement for a couple of weeks should be adequate to again try the 5 mcg of T3.