I use similar tongs but I hold the prey by the middle of the tail. I have never had the tongs struck doing it this way.
If something like this ever happens again just release the object. Once the snake thinks the food is dead it will release its grip. In most cases you could probably leave the tongs as the prey should be eaten and not the tongs but if it is imperative to remove them this would be the time to do it. You probably shouldn't do it by hand though being the snake is in feeding mode.
A lost tooth is no big deal. Snakes replace teeth their entire life. No trip to the vet should be needed. A snakes mouth is very flexible and their jaw is quite amazing. Watch your snake close as it eats and after. You might get to see it reset its jaw. I doubt any damage was done. However if you notice the jaw not seeing correctly and your snake tries unsuccessfully to set it, you may have an issue. Again highly unlikely.