why are you taping your nose? You are very early out from your surgery and your surgeon should be caring for your nose. I would consult your surgeon because you may end up moving your grafts in an unfavorable position.
You are right about your concerns about the grafts potentially moving. However, this is why the nose is usually taped and a splint is placed immediately after the surgery. Those grafts are stitched to the surrounding structures, so unless you are aggressive with touching, gently touching the nose should be ok. I recommend that you follow up with your surgeon and discuss your concerns with him/her.
Recovering from rhinoplasty: restrictions and normal use.
You're right to be aware of your nose as you heal; however, it should not be a source of anxiety.
Rhinoplasty takes time to heal. It is a long process. Along the way, your surgeon can monitor and guide your nose after a successful surgery. It's important to keep your follow-up visits and stick to instructions from your surgeon, which may included restrictions of your activity, diet, blowing your nose, and avoiding trauma. Normal activities: breathing through your nose, walking, and gentle touching are safe.
If you have specific questions, it's best to bring them up with your surgeon. Safety comes first.
It is possible and should be very common to have a rhinoplasty without complications. The grafts that were placed are unlikely to move after the splint comes off 1 week later. I would direct your specific questions about taping etc to you surgeon since they knew what was done.
Best of luck