I think my nostrils are too big for my nose, and that my nose bridge should be higher (Photo)

Nasal aesthetics has both an objective aspect, based on "norms" set by "the Great Masters" and modeling agencies, advertisers, marketers and Social Medial including TV and Movies, and a subjective aspect, based on how you perceive yourself! In your particular instance, it's probably a combination of both!
Your nostrils do appear wider and thicker in their proportional relationship to the rest of your nose. This is esp true for your left nostril, which inserts more laterally than your right nostril. The correction of thick nostrils requires excising a thin slice from between the outer skin and the internal lining and suturing the wall closed so that serum and scar tissue don't collect to thicken it again. Medializing the left nostril attachment could be considered after the above procedure.
Regarding increasing the dorsal height and tip projection, that is more of a subjective rather than objective call and can also be accomplished after discussions with the surgeon.
I hope this helps. Good luck.

The nose is strong and good looking. Whole face is really good looking. You only need an alarplsaty to soften the bottom of the nose, nothing else needed. Some cheek filler will certainly add to the balance of the face.
Alarplasty:
Alarplasty is a very fine and quick procedure that can narrow the nostrils and reduce the flare to soften the appearance. It has other names as well like ‘Weir Excisions’ or ‘Nostril Reduction’. However, it is important to note that asymmetry of nostrils is common and cannot be corrected with alarplasty. Visit the alarplasty website to learn all about it.
Click on the video link below to see the details.
Regards
Dr. J