How long does it take for a toenail to fall off?

I have this kind of weird toenail/toenail cuticle problem with both of my big toes. My doctor says that some yeast probably got underneath my cuticles and ruptured them but im not really sure what the actual problem is. Whatever it is, it turned my toenail yellow and my toes (the 2 big ones with the problem) are now swollen. They both pus and sometimes bleed if something/someone steps on them. So i was wondering, how long will it probably take for the nails to fall off? And how long will it take for them to grow back? Thank you!(: