Cyst, extra cartilage or pre-cancer on nose? (Photo)

Click on the "Web reference" link, just below my response, or go here:
FacialSurgery.com/RealSelf/RealSelf_WildBlueYonder.html
I made a computer morph of your nose, and an animation of the morph, to show the changes that I would anticipate for your nose in truly expert hands, if you wanted that bump removed.
Besides lowering that bump, I elevated the tip of your nose a bit.
It's just rare rare rare to get a cyst in that location. And especially since you've had previous surgery, it should be the cartilage. And also especially since your nose looks a bit long-ish, you'd expect there to be some problem with that cartilage. And more: the little dent out to the side of the bump suggests that it's cartilage. And it just doesn't look like a basal cell at all at all.The woman in the short video just above had her nose shortened in a revision operation. I'd love to hear what you think of the morph.
You should understand that the changes I demonstrated in the morph require very advanced techniques, techniques that most plastic surgeons cannot handle.  Be sure to read the section in the "Web reference" link on how to stay out of trouble while searching for a revision rhinoplasty surgeon.
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 a beautiful nose, and whether he shares your opinion of what constitutes a beautiful 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 a surgeon who understands what's going on and what to do: you don't want to have that bump only partially removed, and if you decide you want your tip elevated, like in the morph, you don't want a surgeon who can't get that done, and then you're looking for yet another operation later!

 The bump on the nose is most likely a bossa which is the result from 2 previous rhinoplasties.  The lower lateral cartilage of the nasal tip can buckle and create a visible bulge, especially in patients with thin skin and older surgical techniques.  A septoplasty is performed in the back of the nose for airflow management and will not help a bossa.   A revision rhinoplasty will  be required to  explore this area, identifying the issue, and correct it.  Revision rhinoplasty is much more difficult than a primary rhinoplasty, so an in-person examination is required.  Choose your revision rhinoplasty specialist very wisely based on extensive experience producing natural results.  

The firm bump on nose is likely a bossae.  This is a visible and palpable protrusion of your tip cartilages, typically result of previous rhinoplasty (or reconstructive surgery) with knuckling of the alar cartilages.  This can be addresses with a revision rhinoplasty such as in the link below.