My left eye is bigger than my right and when I smile I don't think it looks good. Does lack of sleep cause my eye to be smaller?

A picture would be helpful, but I suspect the problem you are referring to has to do with a difference in the position of your lower eyelids. Lower eyelid asymmetry when smiling is a common problem and not likely related to how you sleep. If you like the lower side better, the higher side can be treated with low dose botox injections to help make your face more symmetric.

It’s difficult to say the exact cause without a photo.
Differences in the appearance of the can eye can be related to position of the
eyeball within the socket or differences of the eyelid. Some people have can
have abnormally drooping eyelids. This is called ptosis.

Regardless of the cause, consultation with your local surgeon will help
determine if there is a treatment to help you.

Lack of sleep will not permanently change the shape of your eyes.  Your eyes may be slightly more swollen in the morning due to lying down all night but this resolves during the day.  The shape of your eyes is due to bone structure underneath and all patients have some degree of asymmetry.  See a board certified plastic surgeon if this concerns you greatly.