Well, it looks like you have secondary hypothyroidism...i.e. pituitary failure. The reason I say this is that ALL of your thyroid tests are low, and not just your TSH level. This makes sense with your clinical picture given your symptoms, and the fact you're on synthroid!
One thing about your IBS...it may not be IBS at all, but a side-effect of being hypothyroid....after all, many processes in the body slow down when you are hypothyroid, and this can include the GI tract which can give you all sorts of bowel symptoms.
Thirdly, yes, the radioiodine uptake scan (RAIU) is familiar, and they want to see the integrity of your thyroid tissue. They want to make sure that your thyroid itself is not sick...in this case, I don't think it is because, like I said before, your TSH is low. If your thyroid was sick, your TSH would be high.
Question, though, why did you post this in the liver section?