They sound like they are caused by Graves Eye Disease (also known as Thyroid Eye
Disease) which is caused by different anti-bodies than the ones that caused your
Graves Thyroid
Disease. These antibodies cause a fat-like substance to be deposited in the muscles behind the eyes, which eventually push the eye out of the socket, causing the characteristic stare. Somehow they eye movement also causes the lid retraction you are referring to.
The antibodies can be blood tested for, I believe.