Exposed nasal cartilage. How does this happen? Will I require surgery?

Exposed cartilage without prolonged or significant direct trauma to the septum would be an odd finding. An in-person exam can help to allay your fears. If cartilage is exposed, treatment depends on the extent of the exposure and underlying cause. 
Your deviated septum can be addressed through a septoplasty. Patients with breathing complaints may have some coverage for the septoplasty surgery as part of their insurance agreement.In our practice, patients who gain insurance pre-approval have at least a portion of their septoplasty anesthetic and facility fees paid for by their insurance plan.
A detailed examination will help delineate the best treatment. Consultation with a plastic surgeon certified by the American Board of Plastic Surgery would be the next best step.

Thanks for your question. I have seen exposed cartilage without surgery from trauma, autoimmune disease, infection, as well as nose picking. You must go an be seen by an ENT doctor ASAP for a diagnosis as well as treatment plan.  Do not focus on the deviation of the septum, rather the health of the septum at this time. Ideally, a perforation can be avoided. Best of luck!