I have medical issues relating to my nose where I can't breathe properly and there's a surgery to fix that but it will also fix the appearance of my nose by reshaping it which makes it kind of like a plastic surgery. I can also tell them not to reshape it but it then my facial looks may go down and make me a less attractive person which can cause me difficulty in looking for a spouse in the future. Is it permissible to tell/allow them to reshape my nose?

Yes reshaping the nose is permissible