Is it a safe method to use goretex placed in to the bridge of your nose, and ear cartilage on the tip?

While Gore-tex and other synthetic implants have a higher rate of complications than using tissue from your own body, you are certainly not at any immediate risk.  While there is a higher risk of infection and extrusion - infections can typically be treated with antibiotics and extrusion is more of a long-term issue.  

Whenever an implant is placed in the body, there is always a risk of infection, but in most large clinical series that risk is low enough to make a goretex implant a reasonable choice for augmentation of the dorsum of the nose.  Other issues that may arise with goretex are slight shrinkage of the implant over time and tissue ingrowth that may make removal of the implant somewhat challenging. In general autogenous tissue such as septal, conchal or rib cartilage has the lowest risk of infection or extrusion.