Can I still be an amateur/pro boxer after nose surgery?

Sort of depends on the kind of fighting you do. If you wear head protection, then that's great. If you're always getting punched in the nose, then you might think about waiting until you end your career. 
If surgery seems like a reasonable idea, remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills.  Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon.  

A modern, structural approach to rhinoplasty should not leave your nose weaker.  However if you received a serious injury to your nose after surgery it would be much more difficult to fix and you may not get as good a result again.  Unless your nose is badly blocked I would not advise rhinoplasty until you have stopped boxing.