ChristinaDe
I also can relate to the puffy eyes. This is a symptom that has really bothered me from the start because it’s a constant reminder that I have a “disease”. I kept telling my husband how much I hate the fact that I have an illness that not only affects my mood, mind & body…but my appearance as well. And since the eyes have been called the “window to the soul” – having them change feels even more significant. Plus it feels like I’m wearing a sign that notifies the world that something is off w/ me.
I’ve been seen by a neuro opthamologist who specializes in Graves’/thyroid pts, and a opthalmic plastic surgeon who does as well. They both told me that since my antibodies are low to almost non-existent that my eye issues are probably related to my thyroid levels and not Graves’. That means that (at this point anyway) they’re not too concerned that they will suddenly bulge out or that I’ll develop double vision. But it also means that whenever my thyroid levels (TSH, T4, T3) rise or fall out of range – or even just move, even when moving toward normal – that I’ll see an increase in this swelling. Apparently the swelling begins w/ fluid building behind my eye & sort of spills out to the surrounding tissues. Once my levels normalize AND then stay there for at least 6 months, but maybe as long as a year, I “should” see the swelling go down. To what degree no one knows yet. I’ve noticed all this to be true so far. So now I wait. But I’m w/ you on this one…it’s not a pleasant experience.
Also, I was told to make sure that I wait this out before doing any surgery since there is no way to know if it’ll completely resolve on its own, or just partially & to what degree. Ughh – hate the waiting, but it makes sense. And when the swelling gets worse, they don’t just bother me in the mirror. They ache a bit, they’re dry & gritty, that sort of thing. But they assure me there is hope. Whatever is left after all this can be surgically dealt with! 
But I was also told to call if I developed any vision changes cuz this could mean that a nerve is involved & I’d need to be seen (although they’re not expecting this).
In the meantime, the thing that seems to make the most difference in mine is keeping my head elevated as much as possible. For example, the swelling tends to worsen for several hrs after a yoga class. Also, staying hydrated seems to make the swelling swing up & down a little less (but I’m not entirely sure if they’re related or if that’s just in my head). Seems like you may be onto something w/ the sodium thing as well. I’ve thought the same thing. Would love to hear if you notice any improvement after decreasing your sodium intake!