Why is my philtrum so short? Can I do anything about it?

On many people, the nose is tall in its vertical dimension, and that makes the bottom of the nose impinge on the philtrum, sit closer to the upper lip, and make the philtrum look so short.
Then, when you smile, all those features get exacerbated by the movement of the facial muscles with a smile.
I can't really evaluate what's going on, because the pictures you posted show the bottom of the nose and the lips, but I need to see the entire nose, and how it fits to the forehead as well, to get more details about the overall size and length of the nose.
I'd love for you to see some excellent professionally-designed morphs of what could possibly be done with your nose, and indeed *whether* working on the nose would help what you notice. (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 also, in case you consider a rhinoplasty, 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?

The actual length of your filtering is not really short it's just displaced in such a manner that it look short. Botox can be tried to release some of the muscles that pull lip up. Shorter this release those muscles and reduction of the caudal septum and possibly the nasal spine can improve the appearance.

Hi znoorara,The lower part of your nose cartilage (caudal nasal septum) is inferiorly placed.  A rhinoplasty including removing some of this cartilage while simultaneously freeing the nasal muscles from your lip should increase the length of your upper lip and philtrum.  Be sure to choose your rhinoplasty surgeon carefully based on their skill, knowledge, experience, care and most importantly their natural artistic vision.  Good luck and be well.Dr. PEncino, CA