Question about refractive errors; can you change the eyeball shape like braces move teeth?

Sort of: There are special contact lenses that some doctors prescribe to gradually reshape the cornea. They are often worn at night and left off during the day. If you stop wearing them for several days the eye shape gradually returns to its baseline. Unlike braces, changing the shape of the eye is not permanent. Lasik and other refractive surgeries do change the curvature of the cornea.