Can a punch to the nose do this to you?

Your brother is doing you no thing good by actually hitting you. Unless you're close in age ,weight, height and equal in boxing knowledge, this is not good. If you think you are, then get some good 14 oz. gloves and inexpensive headgear and a good mouthpiece. Then BOX, not fight under controlled conditions with an adult present. You can damage your nose enough, that you could need to have a doctor look it over.