I've always hated my nose, I feel it's too wide especially when I smile. Is it possible to correct this? (photos)

After viewing your excellent set of images let me comment my opinion and technical advice:
-your nose is not a "bad" or "ugly" one, it can be considered an accetable nose, however some enhancements or better said refinements could really benefit you significatively; that is why your nose is very very difficult, it is not a bad nose ranking 9 out of 10 in ugliness... it is a good nose raking 7 out of 10 in beauty and you are seeking around 9 or higher, which is respectable, understandable (you must be a perfectionist in your mind and profession) and feasible... however only but a really top-notch surgeon with reputed skills in difficult nasal tip surgery
-from the technical side I'd begin with the dorsum, itself is a good one, no hump, straight and as first instance I'd not touch it; nevertheless, if we aim to a high degree or refinement on your tip I recommend to lower your dorsum (reduce the distance between nasal dorsum and Joseph's angle at the maxilla) in order to achieve a better ballance facial aesthetics; not a very difficult maneuver though tricky on your nose considering it is just a mere change of dorsum's angle; anyhow an achievable goal
-in static position your nostrils are oversized, so a alar base wedge reduction can be a good option for you, with acceptable but visible scarring at the alar crease; important note: alar reduction DOES NOT correct or address the flare when you smile, that assumption is absurd and lacks basic understanding of facial anatomy and rhinoplasty
-in dynamic contractions your nostrils flare out due to overaction of the levator alaque nasi or muscle lifter of the nasal wing, well, this muscle can be transected or severed to get rid of this weird effect when you smile, strongly recommended and easy to do; in your case you also make a "hook" when smiling due to the action of the depressor septi nasi, another muscle that can be easily transected and freed to avoid such effect
-otherwise your primary and main issue / diagnosis is a bulbous, oversized, overprojected and poorly defined tip (google all these terms); requiring skills and experience of a nasal tip surgeon able to accomplish well done aggressive tip reduction and deprojection, tip domes plasties (plication, Ortiz-Monasterio plasty, etc), eventually tip grafting (Sheen's).
I recommend open approach. Surgical time about 2-3 hours. Difficulty level 7 out of 10 in primary non-ethnic rhinoplasties.

I agree that the appearNce of your nose can be improved considerably. It needs to be shortened and narrowed.  The flare of your nostrils can also be corrected using solar wedge rejections.

 Rhinoplasty for the excessively wide nose with thicker skin etc.  this can be corrected by narrowing the nasal bones, narrowing the nostrils, and refining the tip with possible removal of a small hump. The nose will still be wider when you smile as it naturally does this in all people.  See a very experienced rhinoplasty surgeon who does natural looking noses.