You have to be 18 before you can authorize a surgery. However your parents can agree for you to have surgery before then.
At 13, you are still going through growing. Any surgery like that done at that age is unlikely to produce good results. It will change the way different parts of your nose/face will row and could result in for worst looks then you have now. Most doctors will refuse to do such a surgery (unless there is a medical necessity) until you are older.
It is NOT a five minute job. One of my sons had to have such a surgery for medical reasons. He was laid up for almost three months. He had to have sticks inserted into his nose that were 8 to 10 inches long for much of that time. His whole face was puffed up like a balloon for almost a month. It was extremely uncomfortable, and he was unable to do anything for that entire summer. (No doctor would do the surgery during the school year.)
He had the surgery when he was 14, and to do the surgery they had to open the skin on one side and peel it back. Once it was put back the stitches did not grow like the rest of the skin on his face and left him with a very lopsided nose. (It was done to correct issues with it being lopsided the other way and effecting his breathing.)
He did, however, have the Roman nose "bump" removed at the same time, but now he looks funny in pictures because he is the only person in the family WITHOUT the "bump" in his nose.