Why did my nose split down the center of the tip? (Photo)

The thicker skin with the sebaceous glands were hiding the shape of the pair of cartilages at the tip of your nose. The melting away of the oil glands under the skin reviewed the shape of the tip cartilages and the fact that they were split apart. The good new is that a tip rhinoplasty in expert hands can correct the problem. You would most likely need an open approach to increase the level of accuracy.

Click on the "Learn more" link, just below my response, or go here:
FacialSurgery.com/RealSelf/RealSelf_kellimelissa2.html
I made a computer morph of your nose, and an animation of the morph, to show the changes that are possible for your nose in truly expert hands.
I narrowed the tip of your nose. Also, however, I elevated the tip upwards a bit, and I brought the entire nose back closer to your face.When the tip cartilages are strong enough to make the tip wide, like yours, they are usually strong enough to hold the nose out forward from the face more than we might like, and they tend to hold the tip down, making the nose tip look a little droopy. Perhaps you can see those changes best in the animation. The woman in the short video above had all three of those features, too.The "split" is just the space, the depression, between the arches of the two cartilages. That depression can be filled out during a rhinoplasty operation.
You should understand that the changes I demonstrated in the morph require advanced techniques, techniques that most plastic surgeons cannot handle.  Be sure to read the section in the "Learn more" link on how to stay out of trouble while searching for a rhinoplasty surgeon. You should only have surgery if you are able to make yourself very confident in your surgeon's skills. Read that page very carefully. Most plastic surgeons are quite poor at this operation, and I believe my advice will go a long way toward keeping you safe.
I'd love to hear what you think of the morph. Did it seem to address your main concerns?
Your nose is also a good example of why computer imaging is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. When you see his goals, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. But remember, you're not hiring him for his skills with the computer. The doctor must then show you his before and after photos to prove that he can actually accomplish what he draws on the computer.
In your case in particular, you need to find a surgeon who understands all of the issues I mentioned, and how they fit together, and who can actually accomplish them in surgery.