Is It Possible to Change Shape of Your Nose Through Constant Picking?

picking your nose itself would be very unlikely to change the shape of your nostrils. However, if you pick it constantly enough and deep enough, you could damage your septum, which if it is severe enough to cause a septal perforation, could lead to external collapse of your nose in theory. I would suggest you meet with a doctor who helps you get over the habit of excessively picking your nose before you consider any action to the structure of your nose, as it could compromise any result you obtain from surgery. Best of luck!
-David Mattos, Harvard trained plastic surgeon

Yes it may be possible if you are doing it that frequently so you should try to stop.  Also staph bacteria (sometimes the really nasty resistant strain) likes to live in your nose so picking it all the time may help to spread this booger of a bacteria to every thing that you touch.  Just stop.

Some people do have a nervous habit of picking (at their skin or inside the nose) that can be quite destructive. I have seen patients who have completely picked away their septums (the wall between the nostrils) from picking away at the tissue. This is a pathologic condition, not the usual mild nose cleaning that most everyone does, but rather an obsessive-compulsive repetitive action. If the septum is compromised, it can lead to shape changes (collapse) of the nose, and may be what you are describing. It is imperative that you see an ENT (otolaryngologist) or facial plastic surgeon who can diagnose this condition. You also may need psychiatric help or medication to help this condition before you pursue surgical correction.