Do I have a hanging columella? Can my nose become shorter? (Photo)

Hello and thank you for your question. Based on your
photograph, you may benefit from a tip refining rhinoplasty. Your surgeon can
accomplish this by trimming, suturing, and reshaping the cartilage in your
lower nose. You may also benefit from a cephalic rotation of your tip to turn
up your tip slightly and address your columella.  Make sure you specifically look at before and after
pictures of real patients who have had this surgery performed by your surgeon
and not just a computer animation system. 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

 From the limited photographs presented, it appears that there is a hanging columella present which can be reduced. Reducing the columella will shorten the nose in the vertical axis. To prevent it from drooping  when smiling requires releasing of the depressor septi ligament. For more information and  before-and-after many examples of reduction of the hanging columella, please see the link and the video below 

On your side view I do not see a hanging columella.  When you smile your septalis muscles create more of the look of a hanging columella.  This can be corrected by a rhinoplasty, and even non-surgically by injecting some Botox into the base of your nose to weaken these muscles.  I would recommend a rhinoplasty and perform primarily a tip plasty.  That would involve thinning and rotating your cartilages to give your tip a more refined look.