What's the chance of having a successful revision rhinoplasty with a piece of cartilage hanging in my nostril?

I see a few different areas to improve on your nose. That's actually good, not bad: the more items to change, the more likely the patient is to see substantial improvement and be happy with the overall result.
You have that remaining bump on the bridge. The tip of your nose is strong in its forward projection away from your face. At the same time as moving the tip back closer to the face, the tip could be elevated, so the nose doesn't look so long-ish. The tip looks wide from the frontal view.
The very most upper part of your bridge, the part between your eyes, is strong in its forward projection, too, and could be lowered. Excess strength up there gives the profile the appearance of a Roman statue. Search Google for "Roman statue face profile" to see what I mean.

How *much* to elevate the tip, or deproject the nose, or make the other changes? 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 better just 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 really 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 the surgeon has that information and judgment best.)

Finally, 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 it also discusses how to take photos that are best for online evaluations.

And for those who have had previous surgery, it also discusses how to tell whether your first surgeon should be performing your revision.

Hi,
Revision rhinoplasty is nearly always an option if done right and in the right patient. What I mean by that is that many things can be corrected, but may need rib cartilage for example to rebuild the nose. If the patient is motivated and willing to do this type of procedure then it can absolutely work and have great results. It is very rare for the nose itself to be so unhealthy that revision is too risky, and in those patients for which there is moderate concern for the health of the nasal soft tissues there are other things that can be done to help reduce the risk (fat injections, hyperbaric O2, etc.)
With regard to the cartilage hanging inside the nose, this would require a detailed physical examination to determine what is going on there. I recommend speaking with the surgeon who performed the surgery first to see what the initial assessment is and if anything needs to be done. I think a revision surgery would potentially be an option for you if you wanted to seek it out. Make sure to speak with a specialist who does a lot of revision rhinoplasty as it is more complicated than primary rhinoplasty in most cases. And of course, make sure their credentials include board certification in plastic surgery or facial plastic surgery. I hope this helps!

In my opinion, your dorsum is too high and the tip of your nose projects too much. A rhinoplasty performed by a well trained surgeon can fix it, as well as the cartilage hanging.