I think I remember seeing some nice eye masks at Bed Bath & Beyond, but I might be mistaken. Those dinky little satin jobbies don't do the trick. They must be thick, and it helps if they are sort of pleated where they cover your eyes. A velcro closure helps, so you can make it really snug. You should be able to open your eyes wide underneath it and not see one speck of daylight.
As for sleeping with stuff on your head... are you too young to remember sleeping in brush hair rollers? Yikes... like sleeping on thousands of tiny needles... but we did it all through high school and actually slept. Amazing.