Is it possible to correct a crooked nose after a long time?

Yes. Yes. Rhinoplasty is the most complex facial cosmetic procedure. Make sure your surgeon is an ENT surgeon or facial plastic surgeon.
Yes. It would require an actual rhinoplasty though. When a nose is freshly fractured, it can be reduced and set to close to what it was. After a long time, a surgeon has to freshly break bones of your nose and reset it to correct it.