OK this is going to sound odd, but what helped my eye area was doing the goofy face exercises from a 1950's Jack laLane video. No kidding. Built up a little bit of muscle around the eyes and this 'lifted' and made it look less skeletal, more cushion. Dark circles also gone but I don't know if that is the exercise or eye cream or what.
Try the two eye exercises he does here and if it works for you, keep doing it a few times a week:
Jack Lalanne - Face Workout 1 of 30 - YouTube
And yes, you should get the thyroid more thoroughly tested, and treatment if you need it, because that can hurt you more than just having sunken eyes.