Can Trying to Mold Nose with Fingers Cause Permanent Damage?

Cartilage has "memory" and is hard to mold.  Usually surgical intervention is needed.  If you want to change the shape of you nose, best to see an experienced rhinoplasty surgeon.  

The upper and lower lateral Cartilages are poorly vascularized, flexible structural elements of the nose.  Absent of surgical intervention, the possibility of changing their shape with manual pressure is unlikely.  After Rhinoplasty, I believe in some form of surgical molding in the taping and casting process (by the Surgeon) but generally do not encourage patients to participate in this process.

Have you had nasal surgery?  We actually recommend molding-type exercises for some of our rhinoplasty patients after surgery in order to help refine their results or speed their recovery.  This molding typically targets the edema (or fluid from swelling) still trapped in the tissues after surgery.  The cartilage is less likely to be molded itself, but it is possible given a relatively constant pressure and prolonged time period.  I would be surprised if you caused any permanent damage to your nose at this point but would recommend you carry out any further molding under the trained eye of a rhinoplasty surgeon.