Will filler under columella lift the tip? (photo)

I know you mentioned a rhinoplasty wasn't on your radar right now. But I'll give you some ideas in case it becomes more of a possibility, since filler can't help with what you have.
Your nose is long, with a drooping tip, like the woman in the short video that I posted with this answer. The tip needs to be elevated, but you know that already.
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. Three-quarter 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.)
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. 
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?

 I recommend getting a formal evaluation with a cosmetic dermatologist to go over your desired results. Facial fillers like Voluma, Restylane, and Juvederm along with Botox can be used to improve the symmetry of the nose and lift the tip; however, it won't make the nose appear smaller. Surgery would be needed to improve the nostrils or overall shape. See an expert. Best, Dr. Emer