These questions are ones that your friendly pharmacist is ready and willing to answer. I find pharmacists to be among my favorite professionals.

(No, I aren't one.... lol)
I think they will tell you to absolutely NOT store your Armour or Levoxyl in the fridge; it's far too humid in there for things that should stay dry. You should probably store it in the coolest, dryest place in your house, in its original pharmacy bottle. I keep a week's worth of mine in a pill minder in the vicinity of where I take it each day and the rest of the script in a cool, dry cabinet away from the light.
Levoxyl has a checkered history of recalls for being subpotent. They just finished a lawsuit over that very issue, maybe two months ago... not much longer than that, I don't think. You could ask the pharmacist whether they've gotten other complaints about symptoms returning after refilling a script. Maybe your refill even came from the recalled subpotent supply.... Could happen. Someone reported in this forum a while ago that she had finally figured out why her levels kept fluctuating so badly.... Her pharmacy didn't move much Armour, and so it was using outdated product to fill scripts.
Of course, it could be you need a higher dose. But you should always check out the other possibilities too.