Would it be possible to pull my nose down but also raise how far it sticks out? (Photo)

The areas that you described and would like
improved can be addressed with a subtle natural appearing rhinoplasty performed
by an expert artistic plastic surgeon with extensive rhinoplasty experience. Keep in mind that following
advice from a surgeon on this or any other website who proposes to tell you exactly
what to do and how to do it based on two dimensional photos without examining you, physically
feeling your tissue, assessing your desired outcome, taking a full medical
history and discussing the pros and cons of the operative procedure would not
be in your best surgery. Natural appearing results need to be individualized
and what is appropriate for one patient is not necessarily the best for someone
else. I would suggest that you find a surgeon with extensive ethnic rhinoplasty
experience certified by the American Board of Plastic Surgery and one who is
ideally a member of The American Society for Aesthetic Plastic Surgery (ASAPS)
or a facial plastic surgeon (otolaryngologist) that you trust and are
comfortable with. You should discuss your concerns with that surgeon in person.Robert Singer, M.D., FACSLa Jolla, California

Asian rhinoplasty to increase nasal length as well as projection.  It is possible to do this along with narrowing your nostril base. Your goals are appropriate and you should see a very experienced rhinoplasty surgeon for the best results.     

Realself.com is a wonderful platform to exchange general information, but is insufficient to offer reliable specific recommendations that you could get in personal consultation.The changes you're requesting are fine, in millimeters, and all of the related three dimensional relationships and your existing anatomy are important elements to consider in formulating treatment plans.  See one or more plastic surgeons in your area for help with this request.