Bridge bigger than tip. Is it possibly the bone could be more swollen than the tip?

I think what you're noticing is that your nose seems long for your face, where "long" means the distance from where the nose begins, below the eyebrows, down along the bridge to the tip. Seems to me that if the tip were elevated, maybe substantially, it would correct much or all of what you're seeing.
How *much* to elevate the tip, or make 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.

Filler can be used to fill the gap between the upper bridge, which you perceive as too high, and the tip. This would give it a better elegant look without the surgery. You can start with a temporary filler such as hyaluronic acid type and then if you like it, convert to a permanent one such as Bellafill. Alternatively, surgery can still be a possibility.

I hope this helps,
best of luck !!