Hope that you both rest up and feel better soon! I almost always get sick after air travel, usually with some respiratory bug that won't go away - too much recirculated air with too many people packed in like sardines. I know some frequent air travelers swear by those Airborne capsules or Vitamin C boosters beforehand, so maybe I should stock up next time before I travel.
It's important to get some downtime anyway after a busy, tiring (though fun) trip! Snuggling with my dog is my favorite home remedy too - Shadow's not much of a cuddler, but she certainly is intuitive and likes to be nearby when someone is under the weather.