Can you change the shape of your nose by pushing it and moving it around?

Dear Realself user,Thank you for your question, unfortunately it is not possible to shape the nose without any surgical procedure. Only when the nose did not grow fully it is possible to help shape the nose, this is very minimal but possible when a couple of months old.
TAS Aesthetic Surgery Clinic

The shape of the nose is dictated by the size, shape and position of the cartilage and bones on the inside under the skin. No external pressure short of a major blow or trauma that has broken the bones could rearrange those structures.
A rhinoplasty is the surgery that is done to reshape nasal contour. It is done as an outpatient (you can go home that same day) and requires a general anesthetic (meaning you will be all of the way asleep for the procedure). To get access to the deeper structures an incision is made across the collumella (the strut of skin and tissue between the nostrils) and into the nostrils on each side. The skin and fatty tissue is then lifted off of the cartilage and bones. The cartilage is then trimmed and bones broken and repositioned to create a more aesthetically pleasing shape for the nose. The skin and fat layer is then re-draped over the cartilage and bone framework and the incisions closed. The skin will then shrink to match the new shape.  Having a rhinoplasty can help you to bring your nose into better harmony with your other facial features, and nothing short of surgery will bring you lasting changes of nasal contour.

It is not possible without surgical intervention. Your bones and cartilages are mature and without surgical intervention it is not possible to change the shape or size of the nose. In person evaluation by a board certified plastic surgeon would help to discuss your options and possible results. Good luck.