Can Rhinoplasty Make Your Nose Oily?

This is very common and likely due to the spontaneous denervation hypersensitivity and activity of the sebaceous glands that occurs as a normal consequence of surgery. This can last several weeks to months but tends to resolve over time.  

In general, if one has oily skin the swelling may be prolonged and may require longer than 12 months time to heal and see the final result. As it usually takes 6-12 months, it may take 12-15 months.

Yes, it is common and transient. To minimize the possibility of any acne type break outs, start using a facial wash for oily skin at least twice a day.
Regards

The skin of the nose does go through some changes after the rhinoplasty and can be very oily for the first month after the surgery. Topical astringents can help with that.

Changes in skin texture and secretions can temporarly occur after rhinoplasty because normal blood circulation has been compromised secondary to the operation. If you choose, consult with your dermatologist , but this will resolve.