I can relate to you in certain respects in that I have recently given up tea because of the fluoride.
Being English, I grew up drinking tea, and my wife and I got into the habit of drinking a lot of the stuff (unsweetened, with milk).
This is just the normal black tea commonly sold in the UK, probably from India or Ceylon.
I was vaguely aware that it had some fluoride, but I was thinking it was just a trace amount, and nothing to worry about.
And the water isn't fluoridated where we live.
Then I read that the fluoride was likely much more than there would be in fluoridated water. While I don't have your symptoms, I did suspect I was at least borderline hypothyroid, and wondered if the fluoride in tea might be to blame. So I gave up tea. I was also planning to supplement with Lugols, and after doing a lot of reading up, I started this cautiously a few weeks ago. I'm still only on 3 drop per day, but planning to build up to 50mg per day (for a period), as per Brownstein.
No dramatic changes yet, but it's probably early days.
Have you read Lynne Farrow's "The Iodine Crisis"? She has a lot of info in there from a woman's perspective. It's a good book, but surprisingly, she hardly mentions fluoride, concentrating on bromine/bromide/bromate.
I wonder if she perhaps thought that Dr Brownstein (who wrote an intro to her book) fully covered fluroide, so she didn't need to?
Her point with bromine/bromide/bromate is that it's more widely used than we realise, all around us (e.g. in furnishing fire-retardants), and is effectively "hidden". So, of course, it's a worry.
(BTW, we use a teapot, and leave the bags in there until the tea goes too cold to drink any more! And we are a fair bit older than you I think, so we've done the damage over a longer time...I suppose it's possible (by dumb luck) that there are factors in our nutrients or environment that mean the fluoride hasn't affected us too badly yet (or not in ways we can see or feel)).
Thank for relating your story, and good luck in the future.
Edit: Just in case you were not aware, it is normally not recommended to take Iodine supplements in the evening or at night, as it tends to keep people awake.