Does Bump Growing On Edge Of Mole Indicate Cancer?

Hi! I have a mole on the side of my nose that is probably the size of a pencil eraser. It s been there for years but recently, a tiny bump started growing off of the edge like it wants to create its own mole. Is this a sign of a cancerous mole? I also have another mole on the other side of my nose that literally was not there when I went to sleep and was there when I woke up! This one started out very tiny but in the last 3 months, it has tripled or more in size! Made an apt . to have both removed but what is the best method? Thanks for your help.