How long after a rhinoplasty until your nose feels completely normal again?

Depends! Depending on the approach used (external incision or all internal), some numbness may persist for year or even longer. With any rhinoplasty, some swelling may persist for this time also. However, most feeling and function is close to normal by 4-6 months.
Weeks to months. Usually breathing returns to normal or better within weeks to months, but complete healing takes a full year.
A few months. I usually recommend to my patients to go at least 4-6 weeks after a rhinoplasty before any vigourous exercise or strenuous activity. After that, most patients report that they fully feel mostly like themselves in about 2-3 months, but it may take 6 months to a year for the nose to feel "completely normal".
Rhinoplasty Recovery. Your early result will be evident after 3 months. Final results and feeling will appear over the course of 12–14 months, which is the time necessary for complete tissue softening. Areas of sensitivity or numbness will slowly resolve; the tip of the nose will feel stiff and this will improve over the first few months.