Can Botox Be Used to Change the Shape of my Eyes?

If we are talking about the eyelid margin, then no.  To alter the shape of the eye, surgery is needed.  The most common form of this is ptosis surgery and canthal surgery.  Fillers have been used to fill the lower eyelid in an effort to push up a lower eyelid and this can change the eyelid contour.  Please be careful what you look for out there.

Changing the shape of the eyes can be done in multiple ways. Both surgical and nonsurgical techniques can be used. In office procedures like botox and fillers (Juvederm, Restylane, Volbella, Vollure) can be used for subtle non-surgical changes. Surgery such as lateral canthoplasty can be used to make the eyes more defined, almond shaped or slanted. Its important to seek out an experienced oculoplastic specialist to discuss your options. 

By injecting in the lower lid a small amount of Botox, you can loosen up the lid and make the eye look more rounded. You want the other effect, which you might be able to achieve by injecting filler in the upper cheek or tear trough area.  However, it might look asymetric with unilateral filler, so be careful.