Waking up with dry mouth a week after rhinoseptoplasty. Is this normal?

Thank you for your question.
Although dry mouth is uncomfortable and super frustrating, it is very normal to have this symptom 1 week out from septorhinoplasty and it will improve! Dry mouth occurs due to routine swelling of the inside of the nose, which causes you to breathe mostly through your mouth especially while asleep during the first week or so after surgery. Mouth breathing leads to dryness.  As the nasal swelling subsides, usually by 2 weeks, you'll breathe better through your nose and the dry mouth symptoms will go away. 
There are several easy treatments you can try. Drink lots of water to stay hydrated or use lozenges or candy to increase salivation. Biotene is an over-the-counter product that comes in a spray, rinse, or gel and is very effective at treating dry mouth. Try these things as you heal and wait for the nasal swelling to subside and your breathing to improve.