Deviated septum or damaged nose cartilage? I have very soft bendy tip cartilage which sticks out more on one side. (photos)

In your nose there is an asymmetry from differences in the shaoe and position of the lower lateral cartilage, and this gives you more alar retraction on the right side and also is more round on that side. You may also have a deviated septal cartilage, but this requires an examination in person. Get a consultation in person with a Board Certified Plastic or Facial Plastic Surgeon, to discuss the options for a correction on that asymmetry and the possible deviated septal cartilage. The rinitis may and may not be improved, it depends on the physical examination to tell you that.

Its difficult from your pictures to assess for the reasons of your symptoms. But in general, it seems as though you might have some allergies. I would have your nose checked by an ENT and possibly get allergy testing at the same time. The internal structures like your septum, turbinates and sinuses are the reason for your symptoms.  Good Luck!

In person evaluation and series of photos would help. Without clinical exam it is impossible to say about status (deformity) of your septum and other structures inside the nose which can contribute to nasal problems you mentioned. Nose surgery would definitely improve your tip. Good luck.