I was in a bit of a rush when I was trying to take these pictures, so I'll try to take better pictures tomorrow. Her fur doesn't necessarily fall out whenever I pick her up, but sometimes I see little pieces where the fur is sticking out where she may have bumped into something. She is a nervous chinchilla, so maybe she is just fur slipping when she accidentally hits something?
Her diet consists of pellets, timothy hay, and alfalfa hay all by Oxbow (more timothy than alfalfa. I do let her nibble on some of the treat seed sticks every once in a while, but not much because she seems too grabby when I offer her treats. She does eat A LOT though. My other chinchilla rarely ever finished her pile of hay over the course of 24 hours, but my white chinchilla eats a ton. She does live with her kit who is about 3 months old, but even then they eat a significant amount of hay and pellets. She's not as big as my other chinchilla either.
The kit's fur and whiskers look fine though, and so does my other chinchilla who is not sharing a cage with them.