Brownstein has reported that the TSH can become elevated initially with Iodine supplementing. But it is temporary and will come down. Doctors, of course get spooked with this. Warthog's son was born with elevated TSH (she'd been supplementing with iodine) and was put on synthroid because of it (why not desiccated thyroid, I dunno). Her latest post said she was going to start weaning him off of synthroid. She's not posted recently.
I've not experienced it, but I've been taking Iodine off and on so I don't know if that is a factor or not.