Does your nose get taller as you get older? If you have a high nose bridge but a low nose tip what will happen?

As people age there are changes that occur in the nose. Usually the tip of the nose will drop. And this gives the appearance of a longer aged nose.  You need to visit a rhinoplAsty surgeon to discuss your particular condition.  

Definitely the bridge of the nose is an area of change as you progress in development.  This is why, unless it is a traumatic situation, we usually wait until the patient has appears to have fully matured in their facial structure prior to embarking on any surgery that would alter the appearance of the nose.  With a change in the upper third, or bridge, of the nose, typically the nose will appear longer because it appears to start at a higher position.  The low nose tip may need support if it does not change through the maturation process.  Time will tell

Your nose stops growing usually when you do, around age 16.  If might get "taller" in the profile, but Asian noses tend to have a low profile.  I have attached a link of an Asian nose with a high profile.