I hit my nose with a door 4 days ago, should I see a doctor? (photo)

If you are having trouble breathing this can be due to swelling from the trauma, and/or you could have broken your nose. You need to be seen in person to be evaluated.

 Trauma to the nose can cause a fracture of the nasal bones or the internal  septum which can cause breathing problems such as a deviated septum. It is important to go to be evaluated by ENT/ facial plastic surgeon to document the extent of the fracture and determine whether or not it needs to be fixed and repaired. It's also important to document the internal examination of the nose to make sure there's not a septal hematoma.

Yes, go and see a rhinoplasty specialist so that the inside and outside of your nose can be assessed.

From your photograph it appears you may have a nasal fracture.  Please consult a board certified plastic surgeon for an examination and consultation.

If possible, it is always best to be evaluated by a docto rafter nasal trauma. It is unlikely, but if you had a septal hematoma, a small collection of blood under the lining of the septum, this should be evacuated.