Yep. And from what I've read only iodine affects bromide excretion. No other chelator does it. So using ALA wouldn't affect bromide toxicity. If you're really iodine deficient it's reasonable to suppose that even a tiny amount of iodine could get things stirred up, since your body prefers iodine and will eject bromide from the receptors if it has iodine available.
You could try adding more salt and magnesium. You don't say how big a dose you're taking but I had to load quite a lot of both of these when I was first adjusting to iodine. Selenium is somewhat less benign in larger doses, so I never went much above 400mcg/day with that, but I would go quite high with the others, to very good effect. But be careful with these as in all things, and go to tolerance. Read up on it before you decide what to do or how high to try.
I can't speculate on the effect of iodine with thyroid hormone meds, however. I have NO experience with combining iodine with anything besides OTC raw thyroid glandulars. So my advice is to read and educate yourself about the ramifications of taking specific hormones with iodine.
Worth noting (again) is that I did have to chelate with things other than just ALA before I could tolerate iodine. I did a few rounds of chelation and then circled back to iodine + salt and mag loading. Worked well for me but YMMV.
Also worth noting is that Cutler specifically says don't use r-ala for chelation so maybe it doesn't work the same as regular ala. Just tossing that out there in case r-ala is not really a chelator like the r&s form. In which case you could have some kind of metal burden but not know it, if your experience with r-ala is your only barometer for your heavy metal toxicity. I don't remember *why* Cutler says don't use r-ala, only that he says it. I actually take r-ala daily, but not for chelation. I use regular ALA for that.
And thanks for reminding me...time to take R-ALA and ALCAR.