Assuming you have had stable gynecomastia for two or more years, it is unlikely that it will disappear spontaneously. You are lucky that you could approach this problem with your parents. No parent wants to see their child unhappy or suffering in any way if things can be improved.
It would best, then, to approach your parents and ask them simply to take you to a plastic surgeon, preferably one who sub-specializes in gynecomastia surgery for an opinion. This would be for information only -- not a guarantee of surgery. You would then be given all the facts, the pros and cons, and be able to make a decision about possible treatment.
Both you and your folks might even read about Adolescent Gynecomastia on my website captioned below -- it might be helpful to you.
Good luck!
Dr Jacobs