What you are describing sounds more like the chin might have malo (Malocclusion) rather then a fungal infection. You should take your chin in to the vet and get check out. You will need x-rays to check to see if it's just the teeth involved or if the roots have elongated too.
The fur loss on the hands, arms, and chin is most commonly caused by drooling. The chinchilla drools, wipes her mouth with her paws, which causes them to get wet over and over causing the fur to fall out. Fungal infections, like ringworm, normally show up around the eyes and nose, and look like dry flaky skin, not wet.
If it's just the teeth you might be able to prolong the chin's life for a little while with teeth filings, but ultimately, if it is malo, there is no cure. Teeth filing will need to be done anywhere from every few weeks to every few months, depending on how fast the teeth grow. Once there is root involvement though it's really a quality over quantity situation. The top roots will grew up into the skull and end up puncturing the eyes, nasal cavity, and brain. The bottom roots can end up growing down through the jaw, coming out under the chinchilla's chin. It's best to put the chin to sleep before it gets to any of those points.
Just so you know, attachments don't really seem to work on this forum anyway. For pics your best bet is to upload them to a photo share site then link them here.