Yipe! That's a long wait! You might want to try getting the nail clipped yourself. It really isn't hard, especially if you could get someone to hold Emma for you. Or you could hold her and get someone else to clip.

Also, since the vets are all booked up, you could try to find a groomer to take care of the nail. Surely there's a vet or groomer in your area that accepts walk-ins - especially for something like this that'll take two minutes tops (assuming Emma is a little wiggle worm with a tendency to jerk the paw away just before you snip).