What can be done during surgery to improve my nose tip based on the attached photos?

Hello and thank you for your question and sharing your photographs.
The profile suggests that the main problem is the low position of the tip defining points.  It produces an elongated appearance on site view as well as on the oblique views. On the oblique views, in photographs taken on mobile phones it will look worse because of the characteristics of the camera. 
A narrower appearance of the tip to produce a coherent contours with the bridge would require also repositioning of the tip defining points. Maintaining the same placement of the tip defining points in a narrower tip would unfortunately make it appear more elongated. This does not mean shortening the nose, just changing the shape around the tip.
The symmetry is relatively good and you need to bear in mind that nothing about our features is truly symmetric whether natural or with surgery.

First of all, addressing the "droopy" tip is indeed important. The tip of your nose hangs down more than average for a nose, so elevating the tip is important.There are two other issues that I can't quite assess from these photos: one is the width of the tip. It's not a huge ball on the end of your nose, of course, but it might be wider than it needs to be. The other is the "projection" of the tip: how far forward away from your face the tip projects. I can't assess that issue because the photos are cropped just to see the nose, and it's really really important that a surgeon see the entire face with the nose, to assess some features like that. My guess right now is that it would benefit your nose if the tip comes back closer to the face, and then of course bring the bridge back closer to the face to match the new position of the tip.But there is a crucial feature that I can see, that clearly your surgeon didn't address.Your bridge is strong up at the top of the nose -- in front of your eyes, or just below your eyebrows. When the nose is strong there, if the tip and bridge are de-projected (brought closer to the face, as they were in the first operation, and probably will be in the revision), it's 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.
How *much* to elevate the tip, or deproject the nose, or lower the "Roman statue" area? 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. Full-face 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 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?

Hello and thank you for your inquiry!
It looks like you would need a long nose correction, in order to make your nose look slimmer. For the asymmetry you should know that even after the procedure a perfect symmetry is hard to be achieved. It could be improved but still you left side of the nose will be slightly different from the right side. 
Be sure you have an in-office consultation for a better consultation. 
Best regards,
Dr. Ha, Seoul Queen Plastic Surgery, South Korea