Is It Wrong to Clean the Nose with Cotton Stick Few Days After Nose Operation?

The advice regarding nose cleaning may differ slightly amongst surgeons but it is unlikely that you have damaged your nose. I recommend for my patients that moist cotton tip be used very gently around the sides of nasal openings but not at the suture line if any ... this is kept covered in a clear ointment for first few days ... if in doubt contact your surgeon

Not to worry.  Often the inside of the nose gets crusty after rhinoplasty and can be irritating and  impair your breathing.  GENTLE cleaning of the nostrils with a Q-tip soaked with hydrogen peroxide will loosen the crusts and you can very carefully and gently moisten the crust.  It will often melt away or become soft enough that it falls out painlessly.  I have my patients coat the inside of the nostrils with bacitracin after the perioxide cleaning. 

Once the crusts are removed, after 10 - 14 days, there  should be no more crusts and therefore, no more need to clean. 

First it does not seem that you did anything wrong, yet.  Letting the water run off the outside of your nose while in the shower is one thing.  Taking a Q tip into the nostril is another thing.  Most rhinoplasty surgeons would not like the idea of poking inside the nose.  You may cause bleeding, infection or a tear in the suture line.  Always good to ask your surgeon what you can and cannot do, as he knows how he dd the operation.