Is surgery the only possible way to get a different eye shape?

Contact lens therapy: Corneal refractive therapy can also correct nearsightedness and sometimes astigmatism and farsightedness on a temporary basis (1 to 2 days), unlike refractive surgery (LASIK), which is more permanent. It requires sleeping in contact lenses. This can be uncomfortable though, and may increase the risk of infection. LASIK surgery is not performed until 18 years of age.

Change lens power?: I am guessing that you want to change the shape of your eyes refractive surface which determines the power of the lenses for the eye. It would not be a good idea to change the shape of the eyeball for any other purpose as that might compromise the vision. You can change the shape of the eyelids for cosmetic purposes but that of course is also surgery.