Does picking nose 3 months after rhinoplasty harm the final result?

I would advise following up with your surgeon if you have any concerns about this for a proper examination, however, I doubt you have caused any damage to your nose at his point of recovery.

Dear Riionjal,It is very unlikely that you have damaged anything in your nose from cleaning your nose. At three months, there is a considerable amount of healing and it would be hard to cause any damage. That being said, I would follow with your surgeon if you have any concerns. Best regards,Nima Shemirani

Likely the bones have healed at 3 months.  However, if you have concerns you damaged something, you should contact your surgeons office as they may want to evaluate you in person.