Will blood vessels, nerves, and the mucosal lining eventually grow back after rhinoplasty?

Thank you for your question. It’s a tough issue dealing with a dry nose. It is true that nerves, vessels, and mucosal lining regenerate, but how they do that can vary. Most of the time breathing improves or returns to normal, but sometimes it can feel very different.
I’m not privy to the details of your surgery, but two main issues come to mind: the structural changes of your nose after surgery and the function of the mucosal lining inside. If airflow through the nose is changed after surgery, that may dry your nose. Also, if the mucosal lining is affected, it can lead to a change in the production and clearance of your mucus, giving you that dry sensation.
If you haven’t tried it yet, saline rinsing is like mother’s milk for your nose because it helps clear the mucus and moisturize the mucosal lining. It is safe to do even several times a day. Swabbing a small amount of ayrgel or similar lubricants just inside the nostril will help as well. 
I do hope you feel better.