There's this weird liquid that smells awful in my nose which is dripping down to my throat. Is this normal?

Make sure you inform your surgeon so they can perform a nasal examination to see what the problem is.

It depends. If your rhinoplasty ended with nasal packing, there is a chance you may have an infection. If you didn’t have nasal packing, congestion and post nasal drip may be annoying. When something doesn’t smell right after rhinoplasty, it’s always good to discuss with your surgeon. Wishing you well. Dr Joseph 

Post-nasal dripping after a rhinoplasty is very common during the first two weeks following surgery. This is generally due to mucosal swelling and consecutive alterations in airflow. As the aeration is not normal and the lining is swollen, fluid entrapments inside the sinuses or inside your nose can easily happen and lead to these symptoms. Decongestent medication can help to heal this situation. No need to worry, this is temporary unless you have a chronic sinusitis.

You would be adviced to contact your surgeon so that you can be examined. You will need to be sure there is no infection in the area.

Nothing to fear!!  This is all well within normal as there is commonly increased or altered drainage issues from the nose in the early postoperative period.  The only concern would typically fall 1 - 2 weeks following surgery if dissolvable (chromic) sutures were utilized as these sometimes can become colonized and create a localized infection.  But even in that worst case scenario it is easily treated with a short course of antibiotics and all will be well.  You seem to merely be experiencing a minor increase in drainage issues and these should resolve spontaneously or with the help of a simple saline rinse to the nose on a daily basis.  F/u appropriately with your surgeon and have no fear!!

Early after rhinoplasty, the nasal mucosa may react to the surgery with an increased production of fluid giving rise to a post nasal drip. Swollen mucosa will also create turbulence in the airflow. The combination of increased nasal discharge and turbulent airflow can result in small stationary pockets of fluid trapped in the swollen mucosa folds with some bacterial growth resulting in inhaled odors. I encourage you to communicate with your treating doctor but do expect that it will spontaneously subside.