Constipation can be a bugger and be created from lots of different sources: sometimes parasites or yeast, sometimes mineral issues like Magnesium deficiency which can sometimes be caused by heavy metal issues and sometimes mechanical restrictions like a common bile duct that got strained in a fall or car accident....... and sometimes a congested liver.
how much Mag are you taking?
sometimes taking more helps some
I really think Iodine brought my liver issues to the forefront so I had to address them and I am still plugging away at them in various ways.
I will strongly encourage you to keep looking into figuring out how to move your bowels more regularly, like 2-3 times a day....you don't want that stuff in there too long
if the cause is hypothyroid the Iodine should fix this problem in the long run, so you may be going through a reset with your thyroid and yes as you suggested it may be detox too.
sometimes doing regular enemas to keep things clear is necessary as a stop gap until things straighten out......