Yes, iodine can cause problems like this. I had to limit my egg intake to control that. Fortunately I can eat egg, but if I eat it for breakfast for 3-4 days in a row, I’ve got some issues.
Fasano diet is great.
For anyone having DH I’d recommend to start with that, or just elimination diet. Live everything out until the DH symptoms disappear. I ...
For me, cold water shower helps, and having a bath of salty water. I use dead sea salt. It helped.
And obviously - no gluten, no processed food, no eating out, etc.