Is it possible to vertically lengthen my nose a few milimeters?

If it is a slight lengthening of the nose and tip derotation the best option which saves more embarrasing nasal lengthening procedues is the en bloc tip-columella shield graft.

This is possible with a technique called a septal extension graft, which can be used in the case of people with short noses who need lengthening.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search. 

Hello and thank you for your question.  The
best advice you can receive is from an in-person consultation.  A caudal septal extension graft can help lengthen the nose in the right patient.   Make sure you specifically look
at before and after pictures of real patients who have had this surgery
performed by your surgeon and evaluate their results.   The most
important aspect is to find a surgeon you are comfortable with. I recommend
that you seek consultation with a qualified board-certified plastic surgeon who
can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D.
Harvard-trained plastic surgeon