How can you tell if you have a broken or just a bent nose?

Nose trauma. If the nose was straight before, then became crooked after injury, then it was broken. You can't bend the nasal bones ! note-- this needs immediate evaluation by ent. If surgery is needed then it needs to be done within a couple of weeks. Otherwise, the nose will heal crooked and require more complex later surgery to repair.
Broken nose. If you have just injured your nose, signs of a broken bone or septum may include: bleeding, trauma to the skin including laceration, bruising, swelling, bruising that extends under the eyes, pain and tenderness. The bony bridge of the nose may be displaced a little or a lot and somewhat mobile when touched. If you suspect a broken nose, you should seek evaluation with a physician.
Broken nose. If you have just injured your nose, signs of a broken bone or septum may include: bleeding, trauma to the skin including laceration, bruising, swelling, bruising that extends under the eyes, pain and tenderness. The bony bridge of the nose may be displaced a little or a lot and somewhat mobile when touched. If you suspect a broken nose, you should seek evaluation with a physician.
New from injury. If the nose has been bent a long time with no mechanism of injury then it is just bent. If you injured it and the bend came after then it is probably broken. Rhinoplasty can fix both.