Can a collapsed nose heal over time?

Dear rosieIn general, scar contracture and lack of stability of underlying structures leads to longterm changes after a rhinoplasty. This is usually not present after trauma. With the typical nasal fracture, you have displacement of structures but not instability and significant contracture. If at 12 weeks after trauma you still have nasal deformity, you will likely need surgery for correction.

Without photos, it is difficult to respond specifically. Theoretically, though, if you have a collapsed nose, the cartilage has been removed or weakened, and it will not "correct itself." Generally, in situations such as yours, the condition only gets worse due to the lack of proper support or placement. 

 Once the nose has been traumatized, fractured and collapsed, it will permanently stay in that position until a rhinoplasty procedure can make the required changes to straighten it. For many examples of straightening a crooked nose, please see the video and  the link below