The short answer is yes, you can sue the person who punched you.  If you were to bring a lawsuit against this person, you can only reasonably recover money for the any damage the person caused you by punching you.  You will not be able to have them cover the costs of your nose job which was three months old.  Also, in bringing a lawsuit, you often times have to submit several years of back medical records in which case your previous nose surgery would become public knowledge.  Lastly, it would be extremely difficult to collect from this person if they are unemployed.  Bringing a lawsuit is costly and time consuming and you often times have to expose a lot of your own personal information so it is best for you to strongly weight the pros and cons before moving ahead with a suit.