Is there a method (except surgery) to eliminate or reduce a cyst on the vocal cords(in my profile there is the photo of my vocal cords) ?thank you

Cysts: Cysts, no matter the location, have tendency to change in size and intensity but do not go away on their own. There is a casing around a fluid filled sack. Things like irritation tend to aggravate them. To eliminate completely, unfortunately you have to remove the entire sack. This is a surgical procedure. Voice rest, control of any acid reflux or post nasal drainage, can decrease size.