Saws are soooo quick when they bind up and kickback. Glad to see you only mangled the fingers. I had the same thing happen to me 37 years ago just move over to the middle finger being mangled and the ring finger being cut off about an inch.
I was over reaching when my saw kicked back. Dumb, really dumb because I knew better but I still did this. I still use a circular saw [threw the finger eater saw in the trash.]
These two fingers are super sensitive to hot and cold. All the nerve endings are located in the tips of your fingers. Now they tell me.
Be prepared to scream when they take out the stitches – I yelled really loud and scared everybody in the area.
Hurt like heck!