Oh I am so sorry to hear that you are having such a hard time. I don't know anything about
diverticulosis, so I am sorry that I can't be of any help there. It's crazy to hear that your GI doesn't seem to concerned about
a rupture. If it was me, I would just go to emergency and get treated there. When I started flaring a few months ago, my pain was pretty bad and my GI wouldn't give me any sort of pain relieve. I was forced to go into emergency where they treated me there for pain and started me on prednisone, (which didn't work btw).
I do hope you find relieve soon. Take care.