You should have the thyroid checked, but be aware that the bulging of
the eyes has nothing to do with thyroid hormone per se.  Too much
thyroid, to be sure, can make your eyelids go up, giving you a
surprised look, but it doesn't make your eyes bulge.  The bulging is an
effect of Grave's disease per se (and doesn't happen with any other
thyroid disease), and is part of the immune problem (an effect on fat
in the retroorbital space).  When the thyroid is treated (by removing
it or killing it with radioiodine), it doesn't help the eyes at all.
Sometimes they even get worse.  Only surgery will fix them.

                                 Steve Harris, M.D.