What is the earliest time after getting my wisdom teeth pulled out can I get a nose job?

2-3 weeks. As long as the extraction is uncomplicated, 2-3 weeks should be long enough to allow any swelling to subside and allow the gums to heal.
Any time. You can have a rhinoplasty as soon as you feel recovered from your dental surgery. The two operations do not interfere with each other. Assuming you are healthy, the anesthesia should not be risky.
Rhinoplasty. Having your wisdom teeth removed does not preclude you from undergoing rhinoplasty. Be sure to have your nose evaluated by a board certified facial plastic surgeon.