Well, my ex-gf also told me that height doesn't matter and looks is not important. What's important is on the inside. But I never seen a fat and ugly chick dating a tall and handsome man (and intelligent) unless she really makes up for it by being super rich and vice versa.
Do you have a gf? If you don't, you can tell your mom, "that's why." Height counts.
I assume you need your mother to understand because she will be paying for the surgery. Because if not, we live in a democratic society and you can go do LL with your own money.
I think the reason for not having a GF is a good excuse to tell your mother. Otherwise, you can show her charts of how taller men makes more money then shorter men. And if she watches drama, you can tell her that the main characters are always the tall, handsome and smart guy. And the villain or the secondary characters are short. Or you can tell her to loan you the money and after you come back taller and get a new job, you can pay her back. My salary increase by 20% after I came back.
if you need more advice, let me know. I have 28 years of life experience.