Can I fix the “squishy” end to my nose? Follow-up question (Photo)

Your face has attractive features, but what you are noticing is that the cartilage of your nose curves off towards the left, thereby giving you the appearance of a broad, flat, bulbous, ill-defined tip. The good news is that all of this is fixable with rhinoplasty surgery. With careful manipulation and trimming of your cartilage, an elegant, feminine and detailed nasal tip can result.

First, the bump on the bridge. Yes, the bump can be removed, but there are some caveats to that. Often, when a bump is removed from the bridge, it makes the nose *look* longer, as though the tip had drooped. So we often elevate the tip, to offset that perceived change, even if a droopy tip wasn't a complaint originally. 
The woman in the short video that I posted with this answer had a bump somewhat like yours. However, the bottom of her nose points up a bit, and the bottom of your nose -- the line from the corner where the lip meets the nose out to the tip -- your bottom part is somewhat lower, parallel with the ground. You don't have to raise the tip like a miss piggy nose, but if the tip isn't elevated a touch, and the bump is removed, your nose would look too long, and you'd be trying to figure out why it looks worse without the bump.
I'd love for you to see some excellent morphs of what could possibly be done with your nose. 
Then, that tip. We don't change noses because they are "squishy," but rather if, for example, the cartilages are making the tip wide. Or asymmetric. I see how the tip of the nose seemed to curve to the side in one smiling photo, but it doesn't seem to do that in photo #1. Hmm. Although, these photos still aren't well-posed for a great evaluation.
If the tip is squishy because the cartilages are soft and the skin is thick, then there's really nothing that can be done about it.
Hope I'm being more helpful than confusing.
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, requiring 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.
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?