Clicking after rhinoplasty. Could the graft be loose?

Unfortunately, the clicking sensation you describe can occur after columellar strut placement and is a result of the lower part of the strut (at the base of your columella) sliding against the anterior nasal spine. This may improve with time as the complete healing process after a rhinoplasty can take up to 1 year. However, if it persists and is bothersome, I would recommend having your surgeon re-evaluate and determine if a small revision could help correct this. Good luck!

This can occur as mentioned below with certain expressions.  You probably did not harm the result when you pushed on your nose after surgery.  If there are no change to the appearance, not to worry.