Why does my nose look small from the side but big from 3/4th perspective? (Photos)

Your nose looks "small" on the side view because your are not smiling. On your 3/4 view the nose appears larger when smiling. Smiling will dynamically change the shape and "size" of your nose. So, try taking the 3/4 view photos without smiling. You'll see the difference. Best wishes.

Hello and thank you for your question. You are a better candidate for a surgical rhinoplasty.  Based on your
photograph, you may benefit from a tip refining rhinoplasty, which can help reduce the size of your nasal appearance in the 3/4 view.  Make sure you specifically look at
before and after pictures of real patients who have had this surgery performed
by your surgeon and not just a computer animation system.
The most important aspect is to find a surgeon you are comfortable with. I
recommend that you seek consultation with a qualified board-certified plastic
surgeon who can evaluate you in person.
Best wishes and good luck.
Richard G. Reish, M.D. FACS
Harvard-trained plastic surgeon

You are right that with your face relaxed, your nasal side profile is elegant.  However, the 3/4 profile reveals minor issues with the width of your nose and also your tip definition. Ideally, the nasal base would fit within lines drawn down from the inside corner of your eyes (medial canthi). Also, your nasal tip lacks definition- -and this is more obvious on 3/4 and probably frontal view. Adjustment to the base of your nose along with the nasal tip might address these proportion and definition issues to give you increased nasal beauty on your 3/4 and front views. Good luck!