Let's start by having you post your actual thyroid hormone levels, with reference ranges, which vary lab to lab and have to come from your own report. Free T3 correlates best with symptoms, and it's possible that your T3 (hope that's Free, not Total) could be low due to too low Free T4 or lack of conversion of Free T4 to the active Free T3. We'll be able to tell more once we see your actual levels.
While stomach issues are certainly symptoms of hypothyroidism, I've not heard of anything that severe being part of it, though I certainly wouldn't rule it out. Typically, when one is hypo, constipation is the accompanying symptom and when one is hyper, diarrhea would be expected; however, it doesn't "always" work that way.
Have you had colonoscopy to determine if there is something else wrong that's causing these severe spasms? Personally, I'd want further investigation done, before I attribute something like that to my thyroid condition.
Since you've had kidney stones, I'd ask what your calcium levels have been running and if you've been tested for parathyroid condition. Most of us have 4 parathyroids that live just behind the 4 corners of the thyroid gland. They serve a completely different purpose and their only relationship to the thyroid is their location in the body.