But both those brands are high in sugar. Most almond milk is. Not as high as rice milk. I don't know if anyone makes an almond milk sweetened with something other than sugar, unlike some of the older, better brands of soy milk such as Edensoy, which are grain sweetened. It's something to look into, I guess. Pacific also makes almond milk, but again, they go high on the sugar. See if Edensoy or Vitasoy has come out with an almond milk -- they are older, cleaner companies and might have one with less sugar in it. White Wave Silk (now owned by Dean Foods, the largest commercial milk jobber) does have a sugar-free soy, maybe they make a sugar-free almond as well.
Silk brands new almond milk has no soy at all. Blue Diamond does have some soy in it, but not as much as soy milk.
Probably not the almond milk as to the thyroid -- some people have problems with soy -- but check the ingredients to see if there's any soy in it. You also might not like the stuff -- people have different tastes in things. It also could be high in sugar, and some people with thyroid problems will be more sensitive to sugar rushes. Not all products are equal in quality.