Moisturize. I doubt the dryness on the outside is directly related to what is going on inside your nose. Applying a good moisturizer several times a day will likely be of benefit.
Moisturize. Septoplasty surgery may cause some temporary dryness on the inside of your nose. This is usually helped with nasal saline rinses. It should not affect the outside skin of the nose unless you had some reaction to the skin cleanser used during surgery. That should improve with a moisturizer.You should follow up with your surgeon if you are concerned.
Hydrate & Protect. Sometimes after septoplasty the nose is cleaned and a sticky compound is placed on the skin of the nose to allow steri strips and a nasal cast to be applied. When the cast and strips are removed, you can end up with skin dryness and flaking. Make sure you use a facial moisturizer and add a sunscreen of spf30 daily. I would check with your surgeon for their recommendations. Good luck!
Not related. I don't believe that the dry skin is related to a simple septoplasty unless you very recently had the surgery and this is related to any taping or dressing that may have been applied. Try a little otc Hydrocortisone for just a few days and see if that improves it. If not, please go back to your surgeon for some additional insight.