Have I damaged my nose cartilage or tissue? Is this permanent? (photos)

Yes pressure can have an effect but in your case it will be reversible in my opinion. Your skin is good quality as you are young and your nose has thick skin in any case. You cannot alter the shape of the supporting cartilages of the nose with massage, so no harm done. 

Not to fear!! You've done nothing permanent.  This is no different than daily massage or daily agressive work outs.  You can merely change the short term appearance but a few months of nasal manipulation for better or worse will make no lasting change.  I would leave your nose alone for a few weeks to months until everything settles back down.  If you have concerns regarding the appearance of your nose merely consult with a specialist in your area to at least begin the conversation and acheive some answers as to how to accomplish your true long term goals.  Best!