I ran across some information in regards to high aldosterone describing your symptoms, which is from the adrenal glands. I do not recall what the take was on how to correct this exactly but I remember them talking about getting the adrenals strengthened, going off thyroid temporarily, increasing the health of the adrenals, doing a t3 protocol for a short period of time, going back on regular thyroid and then if all else fails there is an RX drug to bring down aldosterone levels if that proves to be the issue.
One thing you might want to consider is taking an Iodine supplement even whilst doing your normal thyroid meds. I have read many sites where they recommend not to use it whilst using thyroid meds, that is absolutely not a good idea and will lead to loads of issues in your bodily functions because Iodine is needed by the whole system not just the thyroid.