Cat paw foreign object?

Hi, I have a 5 month old long hair tabby mix. She's adopted, and came with her shots, dewormed, and deflead. I am currently moving so she is staying with my boyfriend at his house. The weekend I moved her in I noticed when she was playing with me her paw looked like it was cut. So I picked her up and looked at it closer. The paw pad on her front right foot seems to have a weird object protruding from from it. It looks and feels almost like finger nail material. It almost looks like a scale coming out, I've cleaned it and touched it to see if it bothers her when touched. She had no reaction to it other than her being annoyed that her paw was being held. She walks on the paw with no limp or such. I asked a vet assistant that works me with on weekends and she said to give the kitten about a month and see if it falls off or grows. I have noticed no difference in 'object'. It's been about three weeks now.
I was wondering if anyone has seen this before? She has a vet appointment in a month and a half and I want to be prepared. I also have another cat 7 years old and I want to make sure this isn't something that can be passed along to her (seems very unlikely but I just want to make sure!)
Thank you so much for taking a moment to look at this post!

It looks like a horned paw. If you google it you can read more about them. I have a cat with one on each front paw and I trim them when I trim her nails. I think there kind of like calluses and there not painful or contagious. I'm not a vet though so it's always best to have it looked at again if your concerned.