Yes, it is very common to have pain around the belly button due to gas. IBS can be a very painful, even debilitating condition; you don't have to have anything worse wrong with you to feel horrible right now.
Since these problems have started since getting your gall bladder out, that's where I would lay the blame. Doctors today want to call everything under the sun IBS. You burp, you have IBS. I think hiccuping will soon be a symptom of IBS. To me IBS really means a motility problem of the intestines that has no known cause. Either your intestines dump things out too fast or they empty out too slow. Food allergies, post-gall bladder problems, bad bacteria, parasites, etc. really shouldn't be called IBS because we know what causes those problems and we know how to fix them. Theoretically IBS has no known cause or cure. But doctors lump everything in together, which is a real disservice to those of us who have treatable problems that doctors don't want to treat because they've convinced themselves that we have untreatable IBS.
I think you hurt because of the constipation. Between having stools backed up in there and gas that can't get out because of the backed-up stools, you hurt. I think if you could get your bowels moving again, you'd probably stop hurting.
In addition to looking into the bile salts, there is a product called Equalactin. It is located in the bowel products section of most major drug stores (I've found it at Walgreens and I think CVS too). It can be hard to spot, but it's in a white box with a red tab top and red sides. It is a type of calcium that's supposed to be good for IBS symptoms because it both soaks up excess water and draws water into the bowels. I have always tended to be slightly constipated, and when I took it (chewable tablets--they don't taste bad at all), I had, as Sarita would say, "picturesque poops", lol. You may be too constipated for it to fix you, but if it helps, that would be an improvement. You might could combine it with aloe vera pills or prune juice and get yourself regular again.
Oddly enough, I found that letting the Equalactin pills dissolve in my mouth cured my sensitive teeth. If nothing else, they're great on that account!