My bird is biting it's foot and i think it is broken and dead?

When i seperated my zebra finch because the male was plucking her feathers, i noticed that today he keeps viciously biting his foot and now i believe that it is broken, and possibly dead with no feeling. My mom said it's going to die soon except it looks healthy. She refuses to take it to the vet, and now i don't know what to do.... i think it's going to die soon. HELP!