Can I Get Surgery To Turn My Round Eyes into Eyes With An Epicanthic Fold? (photos)

Do NOT get epicanthal folds. It would not look right. You can get more almond shaped eyes without messing with the medial canthal folds. See following link.

I do not recommend you carry out such an undertaking.  Looking at your photos, I don't see anything wrong with the same of your eyes.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons.

You have bilateral upper eyelid ptosis with compensatory brow elevation. This affects how your upper eyelid looks.  You could have your upper eyelid fold beautifully enhances by correcting the ptosis and making a hard upper eyelid crease.  This is not the same as an epicanthal fold, but it is an upper eyelid fold and you will be happy to have this restored.

Thank you for your question. There are surgical options to change the shape of your eyes. I suggest that you move forward and consult with a board certified facial plastic surgeon whose office offers Facial Cosmetic Surgery Imaging. The computer programs are remarkably accurate and can educate you on what will be done and exactly how the surgery will be performed to create the best desired results for your unique image. It gives you a visualization of your predicted results. 
Best wishes,