This sounded so familiar that I had to relate my story. I'm not sure if this will apply to you or not but it may provide some insight.
I started eating gluten free just over a year ago. What I didn't realize at first is that by avaoiding the whole grains that I had been eating before I had decreased my fiber intake a lot. Apparently I already had diverticulitis. When I ate things like grits, popcorn, corn on the cob and ground flax seed I got the same type of intestinal problems that you had described. Things like seeds, kernals and I guess the graininess of grits caused me to have diverticulosis (an infection formed in the pockets that diverticulitis makes.) Although it isn't related directly to my gluten intolerance it is an indirect result from not eating enough fiber in my diet because the gluten free foods don't provide enough. Since then my Dr has said to get 20-30 grams of fiber daily and to avoid nuts, seeds, corn kernals and grainy things that may cause another infection.
I hope this helps.