What could be the cause of a nose tip changing shape with an unexplained lump and is rhinoplasty the only solution? (Photos)

An examination would be necessary to determine the cause of the bump involving your nasal tip. Based on the thin quality of your skin, it may be visible tip cartilage, rather than a cyst or papule. Consider visiting a rhinoplasty specialist or a reputable ENT specialist for a second opinion. If your dermatologist tried to perform a shave biopsy of nasal tip cartilage, that could have left an undesirable result. Hope this helps you. Dr Joseph

Dear Jm48 in Los Angeles, California:
Your history is very helpful, as well as the photographs.  It is not likely your nose has had a change in architecture.  Rather, this is much more likely a minor problem within the skin.  Either a plastic surgeon or dermatologist can help resolve the issue.  An examination is warranted and it is highly likely that the problem can be eradicated. 
          Best wishes
Robert Kotler, MD, FACS 

All I see from your photo is a small milia that can be popped by your dermatologist. Please provide more photos.