I don't have the Mirena, and what you're describing is the reason why.
I was researching IUDs last year trying to decide which route to go. I read a LOT of forums with people that had it, and read some really disturbing things that are, of course, not official side effects. (But seem to be pretty common, nonetheless)
Most of the negative feedback involved issues kicking in between the 2-3 yr mark. Inexplicable weight gain that can't be lost is one of the main ones. And in every case I read, as soon as they took it out, they were able to lose the weight. I also read about depression kicking in, fits of rage, exhaustion, etc... In every case, they'd been to the doctor mutliple times with no explanation for what's happening. The last resort was the Mirena, and once it was removed, everything went back to normal.
There are lots of people that are fine with it and never have issues. But there is definiltely a group that have a reaction to it after awhile, and those are largely undocumented.
I wound up choosing the ParaGard, instead of Mirena for those reasons.
PS: thyroid issues are very common for women after birth. And that may be your problem. But if your levels are checked and they're normal, I'd look at the IUD.