All three of my kids were MPI so all dairy bothered them, even butter or dairy hidden in things. But it wasn't that they were just causing gas, there were a myriad of other symptoms. Tbh I never pinpointed any foods strictly that caused only gas.
A lot of women do get a period while bf - I did 1 out of 3 times but at that point I was mix feeding (though I mix fed with all three so not sure why this last time I got it sooner). Mine was super super heavy, but thank goodness the next one was not so bad!