Having veneers done won't affect your rhinoplasty. But you want to make sure you can sufficiently breathe through your nose for the dental procedure. You won't be able to breathe through your mouth much while the dentist is working on you. You may want to wait more than a week between procedures to allow the swelling of the rhinoplasty to go down so you can breathe properly.
Not so much that we could damage your new nose job, but it may be a breathing concern. Usually after a rhinoplasty, the plastic surgeons likes to have their patient have their nasal pressure packs (nasal rockets) in their nostrils to aid hemostasis and to keep your septum straight for at least a week and sometimes longer. With those in your nostrils, you’ll need to breath from your mouth. Not a good idea to have any dentistry done while you still have your nasal packs in your nostrils as we dentists usually need our patients to be able to breath out of their noses as their mouth tend to fill up with water while we are working on their teeth. Not alone veneers will need grinding of your natural teeth. If you want less working time in your mouth, then look into Lumineers veneers. Depending on you’re natural teeth shapes and positions, a Lumineers certified dentist may not need to grind your teeth at all.