Sharp tip cartilages one year after rhinoplasty. What can be done to fix this? (photos)

The primary issue that I see is that your nose is still long, where we measure "long" from where the nose begins between the eyes down along the bridge to the tip. So a droopy-tipped nose is "long," and I believe that's one of the issues with your nose. I think you'd be delighted to see some morphs of your nose if the tip were elevated.The woman in the short video that I posted with this answer had the tip of her nose elevated a significant amount in her revision rhinoplasty. Then, your nose might still be strong-ish in its forward projection from your face. The tip can be brought back closer to your face at the same time as elevating it. We call that "de-projecting" the tip. More: it seems that your bridge is strong up at the top of the nose -- in front of your eyes, or just below your eyebrows. Again, I'd need a true direct profile to evaluate that well. When the nose is strong there, if the tip and bridge are modified, it can be important to reduce the strength of the bridge up there at the top, or your profile would resemble the profile of a Roman statue, where the profile of the forehead slides right down onto the nose, without that little dip we like to see in front of the eyes. Search for Roman statue profile to see what I mean. Your surgeon must pay attention to that, too.And yes, the depression between the sharp cartilages can be addressed during surgery, usually by putting something between where a dent is obvious, but not fascia, rather, usually some crushed cartilage stolen from the septum.
How *much* to elevate the tip, or deproject the nose, or lower the upper part of the bridge? We figure that out with morphs, well before surgery. I'd love for you to see some excellent professionally-designed morphs of what could possibly be done with your nose. Morphs could also help you identify what's bothering you, and help you set a goal for the rhinoplasty that's accurate for your tastes. Profile and three-quarter views would be particularly important in morphing your nose. (Side note: in my opinion, morphs should always be done by the surgeon, or he should direct an assistant as she makes the morphs. Morphs should be made with a constant eye to what actually *can* be done in surgery, for that particular nose, and only the surgeon has that information and judgment. Another aside: I also recommend that you not show morphs made by one surgeon to a different surgeon. If a surgeon makes his *own* morphs, you get to see whether he understands the important issues of your nose, and how your nose should be changed. But if you show the surgeon someone else's morphs, and he says "Of course I can make your nose look like that," then you don't really know if he fully understands, or even recognizes, the important changes shown in those morphs. And you don't know if he can make those changes during surgery.)
Remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose needs require advanced techniques, and skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. And for those who have had previous surgery, it also discusses how to tell whether your first surgeon should be performing your revision. And it also discusses how to take photos that are best for online evaluations.
Your nose is also a perfect example of why computer imaging by the operating surgeon 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. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, 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 large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?

It looks like that although your tip was deprojected, it was only minimal.   Your tip  still over projects and although the tip cartilages were trimmed, it has resulted in overly defined edges.   With further deprojection through an open rhinoplasty approach tension can be removed from the tip and the cartilage points softened.   The revision could be limited to the tip, but fascia would not be simple and would not  be the best approach.

Revision rhinoplasty requires exceptional skill on behalf of the surgeon and great communication with the patient about realistic goals and expectations.
Common cosmetic concerns include a dorsal hump, wide nose, sunken nose, irregularities, and asymmetries.
In a revision rhinoplasty, cartilage from your septum may have been depleted and therefore often an alternative source of cartilage is needed, such as from the ear. This is just one of the important differences between primary and revision rhinoplasty that need to be discussed in detail before you decide to proceed with surgery.
In your situation,  you might benefit from tip defining procedures using either cartilage grafting or suturing techniques that would harmonize your nose and create a more natural, elegant look.
Make sure to seek out the care of a board certified surgeon with extensive experience in revision rhinoplasty. Find someone you connect with, who will listen to your concerns and provide you with a framework for what is possible.  
Gary Linkov, MD
Rhinoplasty Specialist
Manhattan