Non-surgical rhinoplasty can address very specific issues: it can give you a straighter, more even nose by removing depressions, eliminating bumps, and even changing the appearance of the tip and nostril size and shape. But it is not a substitute for surgical rhinoplasty and it cannot reduce the size of your nose. From the limited photos you sent, it seems as though the tip droops because there is tissue above it that protrudes. Surgery would reduce that protrusion and naturally elevate the tip. I do not believe that BOTOX will work because BOTOX is for an overactive muscle that depresses the tip when a person smiles. Your trip droops at rest.
I would be happy to see you in consultation to address this in more detail if you like.
Dr. Michelle Yagoda