Do I have an epicanthic fold? What kind of eyelid crease do I have?

Attempting surgery to achieve this would be a mistake.  Especially to achieve Asian looking eyes, your eyes could easily be made to look more Asian with makeup.  The size and shape of your eyes and supratarsal crease (double eyelid) are not beyond the realm of what some girls achieve surgically.  

Based on your photo, your eyelids look quite nice and I would not necessarily recommend surgery.  In some cases and when indicated, conservative blepharoplasty can be performed to improve/ alter the eyelid fold.  See an oculoplastic specialist to learn more. 

Thank you for asking the question. You already have a slight epicanthic fold. If you want to make it deeper then you may want to undergo an Asian blephroplasty or double-eyelid-surgery. You should contact a Plastic surgeon who has experience in creating such folds.Good luck!Regards, Dr. Amit Gupta