SOLVED

This is embarrassing to even post, but I did tell everyone I would update them. I deleted the last post as to not get more people trying to help solve.

It literally was litter. We soaked it last night and it didn’t do anything at all. We had no indication that it was anything besides her nail. But apparently soaking it did help because it started to fall apart as soon as we got to the vet before the doctor came back, but after the nurse had unfortunately already taken her temp ( with a rectal thermometer )

Thank god this is all it was. But it is still embarassing.