Could squeezing the tip of your nose cause permanent damage?

Dear Codywilliam,
Thank you for your question. It is difficult to know without an in-person examination whether the squeezing exercises may have had a lasting negative impact on your nasal tip. Sometimes we do advise patients to do manual pressure and taping exercises after rhinoplasty to help effect small changes in the nose and particularly in localized areas of swelling. We recommend you seek further evaluation with a facial plastic surgeon or plastic surgeon who can perform a thorough evaluation and provide recommendations and treatment options to best address your goals. 

It is not possible to say whether you damaged your nose without formally examining you.
It is unlikely that manipulation of your nose in the manner that you described can correct a droopy tip.  However, this is something that a well-performed rhinoplasty can address.  

Thank you for your question.  Squeezing the tip of the nose should not cause any permanent damage, but would not be helpful either. To help improve the shape of your nose, please consult a board certified cosmetic surgeon.