What is this?

What is this guys? Lately he’s been trying to bury his bone in the carpet so I thought it was rug burn? But he’s also been itching like crazy did he do this? He had a vet appointment Tuesday for cytopoint so I’ll be asking the vet about the wound on his nose but I’m scared… also when I check his front teeth there’s like hair stick in his gums I tried yanking it out but Fred hates anything dealing with his mouth he won’t let me