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.

Your rhinoplasty would not have generated loose skin under the eyes.  Typically, once you've had a rhinoplasty that has been done well you start to focus on other things.  Such is life!  But have no fear.  You still have some good options available.  Consider tear trough...

 Closed rhinoplasty techniques can accomplish the goals of making your nose look more symmetrical and remove the bump. All incisions are placed internally with no external incision. For many examples, please see the link below to our closed rhinoplasty photo gallery

 Topical retinoids are acceptable to be placed over the skin of the nose as soon as the cast is removed. Paper tape and a cast are applied across the bridge of the nose for 6 days after the rhinoplasty procedure. In some patients who have prolonged and extended swelling months after the...