5 yrs post op, doctor added cartilage to my nose tip. My nose still have edema & swollen when I touch. Is this normal? (photos)

Yes pressure can have an effect but in your case it will be reversible in my opinion. Your skin is good quality as you are young and your nose has thick skin in any case. You cannot alter the shape of the supporting cartilages of the nose with massage, so no harm done. 

You will find that very few of us will have a splint on after rhinoplasty beyond one week. You might ask your surgeon again to clarify the need, or to confirm you understand the aftercare plan.

A polly beak deformity can arise from scar tissue in the supra tip area or from under dissection. It can also occur with swelling initially. Best to be seen in person.